After combining them 2p2s, you have a 24V, 18Ah battery pack. Your best bet is to replace with something very similar, say 15-25Ah @ 24V. I would use AGM batteries. I don't think it matters very much if the batteries are advertised as starting batteries or deep cycle. As long as they are AGM. AGM are a lot safer than flooded lead acid for areas where people are working all the time. Flooded batteries can out-gas hydrogen, and they can break or tip and spill. In theory, the hydrogen can accumulate and eventually ignite causing a fire or explosion.
There is a very wide selection of 6 and 12V (and even 2V) AGM lead acid batteries available from a wide variety of sources. Shipping can be expensive, though.
If you use two regular car batteries, there are a few things that could go wrong or that you might want to be on the lookout for. First, maybe the charger will time out because the battery capacity is much larger than what it expects. My feeling is that this is unlikely, but possible. This is mainly a function of battery capacity. Same problem could apply to AGM batteries.
Second, as mentioned previously, there is the possibility of out-gassing, spillage, etc. AGM batteries can out-gas but it is less likely.
Third, if you use a much larger battery pack, you could run into thermal problems if you are near the high end of the load for the UPS. When designing something that is battery operated, you can run it pretty hard and let it get hot because you know that the heavy load is temporary, and that the battery will die. But if the heavy load continues for longer than the original designer anticipated, the electronics could overheat to point of failure (or thermal shutdown, if there is one).
Hopefully this will help you make a good decision about how to replace your UPS batteries. I am not trying to discourage you. I am just trying to share the things I would be watching out for.
You already obviously have a good answer from Charles, but I feel like writing so here goes =).
Doing this will cause high charge currents and some degree of battery wear and outgassing. Lead acid batteries, however, are one of the most tolerant battery chemistries to mistreatment of this and other types, so that helps. You could minimise battery wear by using a trickle charger when this happens, obviously, but compared to many of the other forms of battery damage, doing this a few times a year when you need your car boosted is marginal. Just storing a battery in different states of charge can greatly affect it's life. People would be a lot more reluctant to give each other a boost if they had to wait around and trickle charge each other's cars. Instead, we often use a running car to start the other car, no doubt causing high charge currents, disconnect and allow the now running car to charge itself. Automotive batteries are designed with a reasonable amount of this being considered regular use and as a result are designed to be reasonably tolerant. Just charging it at different rates within the battery's spec will affect it's overall life, so absolutely charging it at rates outside it's spec will cause wear.
You may be aware that one of the best ways to damage a lead acid battery is to allow it to reach extreme low temperatures when fully discharged, as this situation raises the freezing point of the liquid enough that it will actually turn solid, expanding and bending/damaging the plates in the process. This often kills the battery in one shot. It is greatly preferable to suffer a small amount of battery wear due to high charging currents rather than allow it to freeze while I find someone to trickle charge it. If you happened to be at home however and you have the spare time, by all means extend your battery life a tiny tiny bit by popping it out, bringing it inside and trickle charging.
Lead acid batteries are also one of the easiest types to recycle(although this is not always done well) and that helps keep their cost low for what they are. Plates can be cleaned/straightened/replaced and acid can be refreshed, meaning that if you had a system wherein repeated over aggressive charging cycles were necessary due to space limits, the right equipment and a regular maintenance cycle would mitigate and minimise the cost of the damage.
The low cost, ease of designing a durable, tolerant, safeish, high current battery with lead acid is a huge part of the reason they have not been supplanted by lithium ion drop-ins or super capacitor arrays.
You may also find this article of interest. A few interesting quotes from it:
"For most all lead acid based batteries—Gell, AGM, Conventional—you can safely select a charger with a maximum charge current that is no greater than 20 to 25% of the batteries capacity. I know this article is about fast charging but I should also mention that you do not want to use a charge current of less than 3% of capacity (think trickle chargers and maintainers).
Try and Remember This Safe Maximum Charge Current Jingle: Rule-of-Thumb is 5 to 1"
This is an indication of how tolerant even the less favorable types of lead acid batteries are to fast charging. Starting batteries in cars tend to be thin plated types with even greater tolerance.
We also have:
"The premium pure lead AGM batteries such as NorthStar and Odyssey that use thin plates and are highly compressed can actually accept a charge rate equal to their stated amp hour capacity! That’s right they can be charged at 100% of their amp hour rating!"
So on some starting batteries they are able to keep the internal resistance so low as to charge in one hour.
So the conclusion we can reach is that while for some battery types especially a trickle charge will be favorable to their lifespan, in general lead acid batteries are much more tolerant to this than you originally expected, with a 10A charge or more being fine for the ~50Ah-ish batteries of even smaller cars. While a higher draw for very short periods of time while batteries equalize or during initial charging phase may cause some wear, it is not likely to be of great impact due to the rarity of the event.
Another thing to bear in mind is that the 75A rating of your alternator describes the capability of it's output, and it regulates voltage, not current. Chances are your battery was chosen for the car to have reasonable draw in these situations.
Edit: To address your additional questions:
Actually saying "alternator does not have current limiting and will hit it with max amps" would have been enough. :)
To say it would "Hit it with max amps" would be grossly misleading and I would not say that. Some current limiting will be provided by the impedance of the internal connections and alternator windings and regulation lag, just not much, and not intentional. During a very brief initial phase the battery will draw a current spike but for a very short period of time due to the fact that the great majority of the power the battery stores is in a moderate voltage range. Due to this, the higher the current spike, the shorter it will be. Some months ago I believe one of the engineers brought up an article during a question about battery balancing, where testing had been done for damage due to the brief high current spikes caused by connecting imbalanced lead acid batteries in parallel. It's bedtime so I won't attempt to dig it up, but you're welcome to search for it.
So in theory, if one-way current limiting device is connected in series to the battery, it would prolong it's life, right?
In theory it might prolong the battery life a very tiny amount, unless you plan to repeat the event many hundreds of times, or perhaps dozens of times if your battery has very low CCA rating (indicating possibly thick plates) or if you had an unusual battery type in your car, like a deep cycle. If you were going to mess with it at all, some testing would be in order and you would probably want to use a full BMS capable of the actual maximum charging current of your particular battery rather than just a current controller so as not to cripple the function of your car. If you had to run your car unnecessarily for 30 mins to bring it up to charge, the cost of gas would greatly exceed the cost of damage to the battery from the brief initial charge pulse, would be more damaging to the trees and animals or whatever, so you would want to avoid that situation. You would also have to figure out how to change the high current wiring of your car and provide power connection posts that bypassed the battery for the situation where you wanted to boost start off a running car.
Best Answer
There isn't enough information to answer this, because your fridge's specs only tell the maximum power draw.
I presume it draws this power when the cooler is running. But it is not running all day. So you should check for how many hours the cooler will run in a day, how much energy it will use... This depends on outside temperature, the quality of the insulation, etc... many variables, and many unknowns.
Say you have a box and you want the contents to stay below 5°C. So you install a cooling system. You also install thermal insulation.
What is the compromise? You could install a foot thick insulation, and then you'd need a tiny cooler to compensate for the losses. Or you could use just a little bit of insulation, like an inch of foam, and use a more powerful cooler.
I'm trying to tell you that your question is a little bit more complicated than you think.
Fridge manufacturers usually do not quote an average power, because it depends on ambient temperature, and also it depends on user habits, like how often you open the door and let warm air in, if you place a warm beer inside and expect the fridge to cool it, etc.
In this case, the most cost effective thing to do is not to store electricity, but to store cold. If you have a power supply available all day except during the night, then the best option is to put a few gallons of bottled water (as thermal mass) in your fridge next to your sensitive medicine. When you have power, the fridge cools the thermal mass. When you don't have power, the thermal mass absorbs the heat flowing though the insulation.
The good thing about a few gallons of cold water used as thermal mass is that it doesn't break down, doesn't need maintenance, it can't fail. Even if your car dies, your fridge dies, and everything stops working, you still have time to find someone who owns a freezer, or buy some ice, whatever. It is low-tech and foolproof.