Natural Mother signed Parental Rights. As Stepmom, can I gain Parental Rights w/o Adpotion?

My husband has had legal custody of their two children since 2010. He's had them living alone with him since 2007. She was in and out of the children's lives as she wished. Her life revolves her wants only. Basically, he gained full-custody due to her own poor choices in life. We have been together since 2007, but dated for 1 1/2 yrs prior to her. We were married in 2012, and the CHILDREN ASKED if I would adopt them, and I'd love to. I have raised them for almost 6 yrs-3 w/o her at all. When we asked birth mom to allow this, she demanded $$. We told her we could throw her in jail for that, She decided to sign the papers later. Now I want to adopt, but I do not $6,000 so I need to find out how to do this on my own(5 kids here now), and if that isn't suitable for our finances; can I be allocated parental rights through their case, with her signed and notarized relinquished rights papers? My HB, myself, the kids, the children's BGM, and BGF want me to adopt, or win parental rights.