Oh Becky! I agree with the others that it sounds like a good idea to take your dad up on his offer. I know you dont want to put him out, but I'm sure there is nothing he would rather do than be helping you out right now. So why not let him?
I'm currently living with my brother and niece because I lost my job and apartment. I feel for you..I know how tough it is and how it takes it out on you mentally, physically and spiritually. Its not what we wanted to be doing or where we wanted to be going, but its not going to be forever.
I think it would take a huge load off of you accepting your dads offer. The kids will be fine and you wont have to worry about the animals either.