[if you're not in a reading mood, please skip to the last paragraph, as it is the most important thing for you to do]
This is a tough one and we don't have a lot of info to go on. Anything I post is heavily biased from my own personal experience with a divorce involving my two daughters over a 2.5 year time span.
You can try as hard as you want to sever all financial ties right now, but guess what, until you're legally divorced or have a legal financial separation...you ARE NOT financially separated.
And when it comes down to it, they're going to list all the assets and all the debts and split them down the middle. In my case it would have been best to get that over with EARLY before she ran up a LOAD of debt, all the while ensuring her income was below the poverty level.
What's best for your kids is not always visible to those who are surrounded with clouds of emotional uncertainty. What's best for your kids is to have meaningful relationships with their parents. Emotionally happy parents make good folks to have relationships with. Those stuck in a stressfull situation probably don't.
Talk to a therapist, have your kids talk to a therapist.
In my case, there wasn't a chance that cohabitation could work out. I have a feeling it won't work well for you either (but I don't know you).
As to the lease...who cares? Ditch it if you have to. Each of you find a new place to live, and make SURE you get to be with your kids half the time. If that's not happening, have your divorce lawyer (that you've already hired, right? RIGHT!?) file a motion for temporary custody arrangement.
If you don't read anything else in this post, please read this: Talk to a divorce lawyer...no, several of them NOW. Keep talking to them until you find one you trust and get along with. Then hire that person. This should not take more than two weeks. THIS IS MANDATORY!
Clem