Hmmm, interesting problem! Don't know if I can help any, but here goes.
When you're using a non-standard charger, it's harder to troubleshoot since no one knows what kinds of weird things you've wired up
You say that you've used this custom charger on the stock battery -- but have you tried it on the same car with the stock battery
after you started having this problem?
If the problem goes away when you go back to the stock battery, it's probably not any loose connections inside the bit, but you should double-check to be sure. A tiny fleck of metal or a hair of solder from a custom connection could be causing a problem when the higher voltage is applied to charge the additional cells that may not appear when charging at normal voltage.
Eliminating that, double check your polarities. I'm sure you have all the batteries facing the same way in the shrink-wrap pack, but you may have reversed the pack during installation. The narrow end is positive. I'd say double check your charger pad polarity, or test with another car, but you've already done that.
If you've shrink wrapped it, you've eliminated one common source of problems -- the button cells making contact with the PCB since they are slightly taller than the stock batt. Make sure your shrink wrapping is intact. If you find any tiny openings use clear tape to insulate it.
The motor running while charging and something glowing on the PCB both seem to indicate that there's too much voltage, either because the charger is putting out too much, or because of some kind of short. If possible, try testing with a different charging setup for the car that's having problems. I use an AC-to-DC adapter, 3.0v or 4.5v, and no more than 500mA absolute max for these tiny cells.
It seems interesting that someone else has had the same problem with that type of peak charger with a different battery setup. Your peak charger may be built for larger cells and may be putting out too much current at that voltage also. The ideal maximum charge rate for these cells is 40mA for one hour, but since no one wants to wait that long I've suggested no more than 500mA for 5 minutes or so. Multi-cell AA packs put out ~1000mA, depending on the types of batteries used. There's no telling what your current the peak charger is trying to put into these things -- it probably starts out charging at a higher rate then drops off towards the end to top off the cell. You say you've set it at 50mAh? Do you really mean you've set the desired
capacity to 50mAh, or did you mean that you set the
charging current to 50mA? A charging current of 50mA should be fine, but if you're setting some desired capacity in mAh, there's no way to know how fast it's trying to fill up that capacity, and it's probably based on the tolerances of larger cells. I'd need more info on how your particular charger works, since I don't have a peak-charger myself.
Removing the motor would fix the symptoms but not the problem. It's probably better to leave it in, so that you know when something's wrong. Otherwise, your only clue may be a loud pop or a sudden puff of smoke.
I would definitely try charging the batteries outside the car first. If they do explode, chances are they would have done the same thing in the car but would have caused more damage. If they overheat quickly outside of the car, your charger will likely not ever charge the batteries correctly, for whatever reason. If it charges them fine outside the car (not excessively warm, batteries hold charge well) but has problems again when putting it back into the car, at least you will know that it is not a problem between the charger and batteries but is likely a short.
Good luck.. post more when you've checked it out.