O.k. - you are treading on thin ice, so be careful. If you are seriously considering petitioning for a new custody placement, you need to talk to an attorney, and follow his instructions to the letter.
Even so, a court is highly unlikely to change a custody determination absent compelling / overwhelming evidence that the current situation is harmful to the child. The court looks at what is in the best interest of the child, but also takes into consideration what kind of damage a move in custody could make. Your DSD would have to move into an entirely different home environment, change schools, and be away from her mother most of the time. That is a HUGE change, one which a court is not likely to make without compelling reasons.
Good enough reasons are not just because you and your DH disagree on your DSD's mother is parenting her, not because of her work schedule or who is picking her up when she is sick. To play the devil's advocate on the picking her up because she was sick - your DH sent you because he had to work. DSD's mother sent her boyfriend because she worked the night before and needed to get some rest. Unless the boyfriend is some sort of molestor, what is the difference?
To play the devil's advocate again, you are arguing that DSD's mother is working the night shift which is detrimental to the child's development / grades / who she is hanging around with. But your DH is in the military and has recently been deployed - he could take a job at McDonald's so he wouldn't have to be away from home. But that just isn't reasonable for him, just as doing another type of nursing may not be reasonable for her.
Good enough reasons are her mother doing really bad stuff like getting involved in drugs or leaving a young child alone for extended periods of time, etc.
Please take a good hard look at the situation and consult with an attorney before you take the step to petition the court. Maybe some sort of mediation or therapy might work better to solve the issues you have with DSD's mother. Take a look at the link below.
Good luck. Your DSD is lucky to have a step-mother who loves and cares about her as much as you do. Wishing her much success in the future.
http://www.legalexplorer.com/legal/legal-QA.asp?Sid=9&Qid=1#A13
Denae