So much of this depends on your relationship with your brother in law, right now. If you have pretty decent communication amongst you, I would be upfront with him. Empathize with him that you understand things are chaotic for him right now, but that you need to know what is going on, or else you put yourself in some financial strain. And I wouldn't be too proud to talk about it in that way, because I would hope that someone would understand. I mean, if a substantial part of their income was being with held, for an indefinite period of time.... they'd be anxious too!
As for the ongoing care and discipline, etc. Again; what are things like now? Is it a pretty decent relationship? Do you feel like you could talk to him (or the mom) about possible issues? Do your standards for parenting, etc match up? Basically, if you interviewed him; would you accept him as a client? If you're feeling wary now, chances are things aren't going to get better. Personally, I would put a timeline on it. I can watch So-and-so for 3 months, then I will need to fill the space.