From the information provided it sounds either like a faulty battery or a very high current drain from the equipment - or both.
Update 1 : Having seen the most impressive photo, my prior assessment stands. This would be extremely unusual. A large amount of energy seems to have been involved. If there were 3 or more batteries in series (were there?) and one was reversed this may happen as the current would be driven through it backwards.
This strongly suggests a bad battery - possibly a counterfeit one.
Update 2:
We now know there are two batteries.
This is less than the 3 minimum needed to drive current backwards through one battery so the back discharge mode seems unlikely.
it is still possible with one well charged battery and one fully discharged.
The good battery can effectively reverse polarity charge the dead battery.
Unlikely but possible in this case.
A counterfeit battery still sounds possible.
Prior material:
IR remote controls pulse IR LEDs with short pulses of very high current - possibly an amp or more. Most batteries should either provide this or just gracefully fail to do so. A very poor quality battery or a faulty one MAY be affected by such a load.
If the IR control stayed on for some reason then a continued high current may occur. If this happens the IR LED would probably die. If your control still works with a nw battery then this is probably NOT what happened.
It is EXTREMELY unusual for an AAA cell to "explode" in use. You need to say if it was an alkaline, or NimH or ??? type cell.
Some appliances allow charging of the battery inside the equipment. If a non rechargeable battery is charged it MAY explode. This would be rare and it is unlikely your remote allowed charging.
Aspects worth considering in situations like this:
These are suggestions only - necessarily an incomplete list.
What sort of battery - Alkaline, NimH, other?
Ability to deliver high current may increase chances of "energetic" reaction.
How many AA batteries in remote?
Three batteries are required in series for reversal of one battery to cause significant reverse current flow when all batteries are in good condition. (ie one "forward" battery opposes the reversed battery and the remaining 'forward' battery supplies forward current.
IR remote presumably?
IR remotes often pulse the LEDs at very high peak current levels - far higher than in most handheld devices.
Brand of battery?
Age of battery (time in use)
Was it recharged
Was a non-rechargable battery charged? Can 'cause problems'.
I'm going to address the larger issue of making the system robust and reliable, rather than just focusing on the batteries. The main issues that I see are: ruggedness, waterproofness, battery/charging, and the "chassis".
If I were building these things myself, I would use PVC pipe as the chassis. But more on this in a moment.
To increase ruggedness, I would encase the PCB in "casting resin". Just google "casting resin". Essentially it is an epoxy that you can pour into the PVC pipe to encase the PCB's to both waterproof them and support the PCB against shock and vibration. Casting resin is available from many hobby/craft stores like Michaels and Hobby Lobby. Just put your electronics in the PVC pipe, mix up the resin, and pour it into the pipe. Important Note: casting resin comes in 2 parts and the ratio of the two parts effects how long it takes to harden. The faster it hardens the HOTTER it gets during the curing process. You want it to harden as slowly as possible, otherwise it might get hot enough to damage the electronics. Experimentation with the resin is important to getting this right.
Casting resin will work best if your batteries are rechargeable and fully encased in the resin. However, I wouldn't do that. Batteries behave weirdly when charged. Best case your batteries could get hot and not be able do dissipate the heat due to the resin. Worst case, your batteries build up some internal pressure that can't be dealt with due to being encased. As an alternative, you could use some super-capacitors. The usefulness of super-caps will depend on your power consumption and a variety of other issues, but I've used them for several applications and they work quite nicely. Essentially, supercaps behave like rechargeable batteries except that they don't hold as much power but they can be charged and discharged almost an unlimited number of times.
If you can't use supercaps, then rechargeable batteries with tabs/pins/wires already attached would be your 2nd best choice. 3rd choice would be standard or rechargeable AA's. With AA's, I personally wouldn't spend much time making the spring keep good contact. That is a massive waste of time because whatever you do, it won't be good enough! Instead, your design should take that into account. The best way to do this is to simply put large-ish caps in your circuit so that if the batteries do momentarily loose contact then the circuit will remain powered up.
If you use supercaps or rechargeable batteries then next comes the charging system. You could simply have a connector that goes to a charger. Of course that isn't very waterproof. A cool way would be to have a non-contact inductive charger. Imagine a transformer with two coils of wire. AC goes into one coil and comes out the other coil. An inductive charger is the same, except that one coil is in the base of your baton and the other coil is in the "charging station".
In the best case everything-- including super caps, charging coil, and PCB's-- could be encased in casting resin. With no seams there is no way for water to get into the circuitry! And with everything encased and fully supported the whole thing is very mechanically robust. With a little bit of work, you wouldn't even need end-caps on the PVC pipe. That way your baton would be a simple and smooth rod. I'd bet that you could take this and throw it out of a low-flying plane and it would survive.
Also, Casting resin is water-clear. Your circuit can have status LED's that can be seen through the resin.
Best Answer
They'll be in series. Placing power supplies (batteries or otherwise) directly in parallel is always a Bad Idea™. Voltages are never quite the same, and the batteries' relatively low internal resistance will cause a large current from one battery to the other, which isn't fun for either of them.