After reading your story I would have to say that you should have a very good chance of getting your step-daughter. Just the fact that the mom’s boyfriend is a registered sex offender should be enough. Why does your attorney want to charge $4000 to take the case? You should shop around for an attorney, $4000 sounds very outrageous unless there are some outside issues at hand.
From what you’ve said so far it sounds like the mom is unfit to care for the daughter. See id you can use that angle on your case. Make sure you document everything that you do and happens as your attorney can use this to help your case. I went through a custody case where my sons mom was wanted by the police and I didn’t find out until she was picked up on a warrant from not one but two different states.
The whole time she was on the run moving from place to place with my son telling me that she was looking for work. Well needless to say that now I have my son with full custody and it didn’t cost me $4000. My attorney allowed my to make payments and my total cost of fees paid so far is approximately $1500.
Look around for an attorney that has a better price and is willing to help you on the case. If you have anymore questions don’t hesitate to contact me. Let me know how things go for you.