My former in-laws have legal custody of both my "girls", aged 2 & 4. I am not the biological father of either, however my name is on the youngest's because. The girls have always known me as "daddy" & I have maintained a very active role in their lives, every day.
Recently, my former mother-in-law has cut off all contact with them. I am in a serious relationship, plan to get married, and she is afraid that we will sue for custody, to which I have no plans to do so.
What are my legal rights as far as visitation? Former mom-in-law is threatening that if I petition for visitation, she will sue for child support.
I have tried to settle this amicably, to no avail. Any advice you can offer would be appreciated.

If it can't be settled amicably, then get a lawyer, and go to court.

Since you are not the biological father of one, but may be the LEGAL father of the other, you may or may not be able to get visitation for both. You will, however, probably be paying child support for "your" children if you get visitation, which really is what should happen anyway.

I'm not sure what state your in but in TX some years ago my former ex who was not the biological father, nor was he on the because, managed to obtain full parental rights- standard visitation etc with my child, as well he NEVER had to pay support of any type because he was NOT the bio. This was nearly 15 years ago, may no longer be possible but I know it happened to me. Check w an attorney.