Originally Answered: Can I get custody of my daughter in this situation?
You can certainly file for custody. Whether you would be granted custody or not remains to be seen. They would take all of the negative allegations you have against the mother of your child, and the negative allegations she will present against you, and weigh them. More than likely, a guardian ad litem would be appointed for your daughter and the guardian ad litem would present the judge with what she (or he) sees as the best option for the child. The judge will then rule. Other factors include disrupting the child's life (would it involve a move that would alienate her from siblings, and/or other family members and friends that she is close with?, etc.), who has the most stable home and financial means to care for the child, etc.
At this point, the mother's boyfriend would play little role in the custody battle because he is imprisoned, and therefore not in the picture. It would have been a more relevent factor if you filed for custody while he was in the picture, and frankly they would probably want to know why you did not do so then if you thought he was a danger to your daughter.
Only convictions would matter, as well- if the charges were dropped, then he has not been proven guilty and the allegations can not be held against him in a court of law. The sex with a minor potentially COULD be a weapon in this case, depending on the circumstances. How old was he at the time? How old was the girl in question? But, more than likely it could not be held against him because, again, he was never convicted.
You can request to be notified and involved with your daughter's medical care and education, whether you file for custody or not. Youc ertainly have that right.
Her learning disabilities and hearing troubles can not be used against the mother unless youc an prove that it is a result of abuse and/or neglect.
The allegations of improper clothing could, perhaps, be used if there is some sort of proof (this being years ago, that could be difficult and without proof it is just hearsay).
Her weight could potentially be considered medical neglect and/or abuse, DEPENDING on the circumstances.