Tough problem!! I guess your solution is going to be partially dependent on how devoted you are to your cats. You also probably want to set a good example of how to responsibly take care of animals for your kids....
I have pets too, and my 'pee-cat' recently passed away. First, I'd like to say that taking them to the vet absolutely should be your first step. No question about it. Just to be sure. You also need to figure out which cat it is - it's probably not both of them...
Regarding finding the spot - it can be really tough - maybe on a chair? Maybe it's not even them? Keep the door to your kids room shut in the meantime so they don't return to the 'scene of the crime'.
My cat was peeing everywhere, and after a few years of trying to deal with it by changing litters, making sure she had a clean box, and even giving her a small dose (from the vet) of valium, I was at my wits end. And this was BEFORE kids! For a few years, she actually got her own room because she would be regular in her box if she had her 'own' box (not sharing with the other pushy boy cats) and her 'own' food. But once we had kids, something had to change. Finally, I actually bought her a tall cat cage (cat playpen) like they have at the petstores. At first, I thought it was inhumane and it worried me, but besides having her put to sleep I didn't have any other choices (declawed, old, and unadoptable). In the end, it was the perfect solution. We let her out when we were around, but otherwise she was able to be with everyone, but also had her own situation (food, litter, water, bed) and we kept it by a window so she could look outside. It was an inconvenience no doubt, but so worth it to me. They cost a few hundred $, but can be a good solution. Just make sure it has plenty of room, is tall for them to jump, is kept clean, and that they get out for exercise every day.
Someone else mentioned possibly making them outdoor cats. PLEASE DO NOT do this if they are de-clawed (you didn't say whether they were or not). Personally, I wouldn't do it at all because I feel that an outdoor cat is as good as a dead cat in certain areas. Maybe if you live in a rural area where there isn't much traffic to worry about - but if not, they'd be better off in another home or even humanely euthanized if that's your only out. But that's my personal opinion....
When you adopt an animal, you are responsible for that animals welfare. If they need a new home - that may be best and the 8-year old might actually understand. I'm sure you will do your best.
Good luck!!