Ok, here's from the cosmetologist in me, just know I never got the chance to finish beauty school.
There are, in bottled hair colors (like you get from wal-mart) a compound called metallic salts that are harmful to everyone, including animals, not to mention incredibly bad for your hair. If you're using those, I would find a friend's house where you can do it. If you've bought something from say, Sally's where you mix it with a certain amount of peroxide, then it is probably OK to do it in the house, but I wouldn't get TOO near to the chin's room, or stay in there the whole time its on there. Another thing you can do is to put a shower cap over it while its on. It will speed up the coloring process, and put the fumes to a minimum. Just don't take the cap off in the chin's room. O.O
I also would like to warn you, if you're going to hold them in a twenty four hour period after you've done your hair, I would keep it up in a bun while they're out, so they can't chew on it, or get their faces too close to where there may still be color on the scalp.
Good luck!!