What are my options and consequences of this actions

I am divorcing husband. My husband left the home, “abandonment” per my attorney, I live there with our two young children and I have been paying the house note. We have a separation agreement and child/spousal support is included in that agreement. Due to him being behind on his support I can no longer afford to make the house payment (I have never been late or missed a payment yet). More is owed on the home than its value; my name is on the Deed of Trust, not with the lender. I have read a lot on the internet and have been told various things from my attorney (depending on how I present the question, I sometimes get a different answer). I really need to know all of my options and the consequences of each option (pros/cons). Ideally, I would like to have my name removed from the Deed of Trust, and not have any negative impact on my credit report should my husband not pay the note. All I want is to move on and have a place of my own to raise my children. Thank you for your time.

*I do not want to put myself in a postion where I could not get a home loan on my own now (for much less of a home) or in the near future.

What happens with the house should be contained in your separation agreement. If you want that changed, you need to talk to your attorney about ways to modify that agreement. The lender will likely not release you from the debt without your husband refinancing the property in his own name.