How do i prove best interest of the children?

I STUPIDLY had kids with a man that should not be able to reproduce. I was young and naive. I didn't realize what a loser he was until I had my first child with him. She was born with a disability and he totally dropped the ball when it came to her care and stay in the NICU. Already in the "cycle of abuse" with this man, I stayed with him thinking I was stuck. I ended up pregnant again although on birth control. When my second daughter was born I left him because he beat me senseless. Shortly after I left my ex I rekindled a relationship with my high school sweetheart. He's in the military and he's the answer to our prayers. He's the father my kids deserve in their life. He's my breath of fresh air. He's also in the military stationed in NC. His orders have him here for the next five years but I only have a temporary order from the court to be here until next September. The order is in RI but there is no order of continuing jurisdiction there. My kids real father pays no child support, has no doented work history since the spring, rarely calls his kids, and can not financially afford to even split the cost of travel to see his kids. I want to stay here with my kids. Their life here is significantly more enriched due to all the benefits of being military dependents. They've made lots of little friends and my four year old loves her new school. I need to prove this to a judge...I guess what I'm asking is which areas of a child's well being a judge is most concerned about....please help