You sound like a loving family and your step daughter is lucky to have you in her life.  The facts here add up to a better home for her with you, but if they are enough to ask a court to terminate parental rights, well, maybe not. And if her Mother does not do so voluntarily then that is what you will need to do.  Abandonment may be a ground the court looks at - and you need to check with an attorney in the area on this - but termination has to be court ordered.  It does not just happen under the law.  Good luck.