How do I relocate if we live out of the US and have custody over my children?

I am currently married to my husband of six years whom I am divorcing next week. We had two children together. And as off right now, I have custody of my kids and he has an order for a death threat on a note. He has suspended visits with the kids until a Social study because he later tried to commit suicide and was for a week on a mental hospital. His family have a history of mental problems like Bipolar and Schizophrenia. He is still on meds and receiving help. We been separated for months now and I have a boyfriend who is in the military and he is active. He is paying child support because it’s taken directly from his check and it’s leaving our kids without a house to live. He hasn't paid the mortgage in 13 months or the utilities in 3 months. I am already receiving letters of the house being for auction. He has been saying he will do something be he hasn't. I currently am a full time student with one year left for my BSN on Nursing I don't work because I also help my dad who is Quadriplegic. I don't have a lot of family members that can help me out babysitting my kids until I work. So my boyfriend and I are thinking of getting married to be together and my kids and I move with him where he will be stationed. I currently live out of the country. Is there any way I can prove that they will be better off out of here or any tips on how should I work on this? I need as much help as I can get I don't know much about this. Thank You.