Will having POA allow me to keep my step-daughters if something happens to my husband?

For your and your husband to have full custody of the girls and the biological mother to only see them once per month (supervised), it sounds as though she isn't cut out to be a mother. Even if you are their legal guardian, you should speak with an attorney in your area who specializes in family law. Short of adoption, which I'm assuming the biological mother won't consent to, ask if there is any other way for you to retain legal custody in the event of your husband's death.

When my mom married my step-dad, I was 15 (and my sister was 18) but he had custody of his 4-year old daughter and 6- and 10-year old sons. His ex-wife had them every-other weekend, but often skipped her weekend whenever she didn't feel like having them! My mom wanted to adopt them, but the ex-wife said she'd die before she gave them up (like they were possessions, not human beings).

My mom adopted each of of them on their 18th birthday, when their biological mother could no longer prevent it. But if their father had passed away prior to that, it wouldn't have been a good situation for anyone.

Power of attorney only authorizes you to make decisions on a persons behalf. You need to seek legal counsel for your situation due to the fact you are not a blood relative. Do you and your husband both have court appointed custody over the girls? Unless the mother agrees to have you continue custody if something happens to your husband then I cannot see how you could legally pbtain custody of these children. Is adoption possible?