Chances of adopting a baby that may or may not be my husband's child

An ex of my husband has a 2 year old son who she says is my husbands child, he has accepted the baby and been financially supporting him since she told him about the baby at 6 months old, although the woman has convienently missed many DNA tests, and since my husband and I began dating has not allowed visitation at all. She is now claiming to be pregnant with a second child that is supposedly his. She has verbally agreed to allow us to adopt both children instead of risking a fight for custody- she has had a previous child removed from her home for neglect and her drug use and she has a noteable record for drugs prostitution and theft as well as been on public assistance with no job for over 3 years. Is it possible for my husband and I to adopt simply as a new couple and not as step parents since there has been no establishment of paternity- no DNA test done and he hasnt signed a birth certificate. After all her requests for money we are hesitant to go about a DNA test now as it would simply entitle her to child support and give her reason to change her mind about us having the children. My husband is in the military and I'm a stay at home mom to our kids and part-time student, his permanent address is in MD, although we are moving to Florida where the mother and children are for the entire process, we have only been married 2 months but have dated throughout a 5 yr course. Please help, I need to know if adoption is possible for us or do we have to go through custody battle