So it sounds like you do need to consult an attorney. You should receive child support and possibly alimony, and depending on your combined assets and debt, and if you own the house, it seems reasonable for you to be able to stay there especially if you are the primary caregiver and custodial parent for your children. But you do need to consult an attorney.
As to whether you can do it, yes, you are strong enough to do this. (I stayed longer than I should have, and in hind sight, though I had doubts about parenting on my own and being able to pay the bills, I absolutely was able to take care of things on my own without a support system). If there is violence you need to keep you and your children safe. Ask your attorney for references to a domestic violence program, or Google the closest one to you. They can give you some support as you decide what to do.
Just as an alcoholic parent in the home is a poor environment in which to raise children, violence in the home is never ok and you need to take steps to be safe.
Here are a couple of threads with some information about domestic violence:
About Abuse http://www.soberrecovery.com/forums/...out-abuse.html (About Abuse) How to leave http://www.soberrecovery.com/forums/...how-leave.html (How to leave)