My insurance for another guy's baby???

My soon-to-be-ex-wife just called me this evening and told me that she is pregnant by her new boyfriend. Her and I have been seperated for almost 15 months and we were getting close to having a court date for our divorce case, which has been drawn out due to her moving 2 and a half hours away and one by one moving each of our 4 children to live with her parents. Her and her new boyfriend have no home and are currently sleeping in a camper trailer across town while she leaves our children at her parents house every night. I realize that this will delay our divorce due to paternity issues, but does this irresponsible behavior around our children give me any advantage for seeking primary custody. She is being a great example for our two teenage daughters which are 15 and 14 years old. She is also currently serving jail time every other weekend for a identity theft conviction in which I was the victim. Her boyfriend's case is still in the courts.

I am also curious about insurance issues. My employer recently changed their company policy so that only dependents or anyone living in my household are covered by the company. I was forced to start paying her premium, though she is still technically a part of my employer's insurance plan. I don't think it is fair for me or my employer to have to see an increase in insurance usage due to her iresponsibility. Increased usage means increased rates for everyone. Can I come back later and require the father of the child to pay all the bills caused by her pregnancy since technically it is his responsibility?

Any advice, legal or otherwise would be appreciated. Thanks.