Is your home currently listed? And, if so, what has the response been? Have you talked to your lender to see if there are any other options available to you?
If your house is heading to Foreclosure and a Short Sale is not an option for you, you might want to consider talking to your lender about offering them what is called a "Deed In Lieu Of" which means that you will give up all your rights to the home and they will not Foreclose on the property. It is still a very damaging thing to your credit, but not quite as bad as a Foreclosure would be. You might then be able to negotiate your move out date.
If you have not looked into the possibility of a Short Sale, you might want to. I am a Short Sale specialist and would be happy to sit down with you and help you and your family evaluate your options.
As for when you would need to move out... the lender is going to want to take posession as soon as they can after they take over ownership. I agree that, if at all possible, you don't want to try to stay in the home until the last dog dies.
If you are certain that a Foreclosure is imminent, then I would suggest that you look into finding your next place to live sooner rather than later. First of all, you might be able to beat the credit reporting which will make finding another place to live easier. And, you and your family probably could live just fine without experiencing an eviction first hand.
I know what a trying time this is for your family. And, if you will allow me to, and if I possibly can, I would like to see if I can help. Please feel free to get in touch with me either via cellphone or send me an email. You can reach me via email at Tisza(at)HomesByTisza.com.
Take care and good luck, I will send you good wishes.
Tisza Major-Posner, Realtor, Keller Williams (909) 837-8922