Electronic – Would splicing existing wires (from charge controller to battery) to connect an inverter work, and is it safe

Electricity isn't simply on or off... you're missing the quantity of electricity which is measured in Amperes (Amps for short).

So, while your UPS is charging, it's using lots of electricity to charge your UPS storing a large amount of power as well as the relativity small quantity of electricity powering your house.

When the power is switched off, your UPS is just providing the relativity small quantity of electricity for your home appliances.

So, in the space of time it takes to charge your UPS, your electric company will charge you the cost of 8 hours worth of electricity, plus 2 hours of normal use, plus a tiny bit extra for the inefficiency of your UPS.

If you do this, it will likely cost slightly more than you are paying now, due to the UPS inefficiencies.

I have an RV that I've done quite abit of electrical work, so I know where you are coming from. To start, let me make sure I understand what you are trying to do. Take a look at this block diagram:

I believe the only information I left off is the 7A max for the charge controller(s). To start, let me bring up the topic of this related question: Charging Lead Acid Batteries in Series. It is not the best idea to charge these batteries in series, but it is commonly done without much issue. However, individually charging the two separate batteries should be better for them. This charging technique is commonly incorporated in more advanced Lithium battery systems. You are almost doing that with your setup...

Your charging sources are not identical which could pose problems. Even though the charge controllers may be identical (6V output), the power sources are not. The two solar cells have different characteristics meaning they will output different amounts of power. It is possible that the charge controller could be set to output a constant current just so long as the input stays above a certain level, but you did't specify the type of charge controller. Most of the ones I have seen are cheap without much concern for proper battery charging.

Another bad point is that individual cell charging systems also handle the load output from the batteries. I don't imagine yours will be doing this.

This is a problem because if the batteries are not charged equally (at the same rate, to same level of charge) their performance will be severely deteriorated.

Another thing to think about is the internal RV converter/charger. This is the device that converts shore power (120V AC) to 12V DC to power your internal lights and fans as well as recharging the battery. The stock converters on most RVs are abysmal at recharging batteries. They basically pump a high amount of amps into the batteries nonstop, causing them to rapidly boil over requiring you to constantly add more distilled water. The best chargers use multiple states: high current, normal, and trickle. During charging times, the converter actually powers all of the 12V stuff, and the current I_RV is reversed through the batteries to charge them.

The reason I bring this up is that you will potentially have multiple charging sources if you have everything on at once: 1 12V charger trying to charge the 2 6V batteries in series, and the other 6V chargers trying to charge the two 6V batteries individually. This will most likely damage the batteries, chargers, or both.

I don't quite know what you mean by this:

Or do I have splice the wires and use only one charge controller?

But it sounds like you mean charging the two 6V batteries in parallel with one charger while they are connected in series to create 12V. This doesn't make the slightest bit of sense. It is possible that you could connect the two solar panels in parallel and feed them both into one 12V charge controller to charge the two batteries in series, taking note of my previous comments about doing so.

Here is some information about the work I did to my RV electrical system.