I think the tougher point would be the legal custody part. I think the physical part is just to have moved in with her father, which she did. Not all the time until she turned 18, it is enough if it was just for a while before she turned 18. The thing is that at some point in time she had to comply with the requirements of the child citizenship act which are:
1. Have at least one American citizen parent by birth or naturalization;
2. Be under 18 years of age;
3. Live in the legal and physical custody of the American citizen parent; and
4. Be admitted as an immigrant for lawful permanent residence.
So, from your information it seems she met all the requirements, except perhaps the legal custody. However, I don't have expertise on how stringent is the legal custody requirement, but in many cases I am sure it involves having divorce papers, legal custody papers and things like that. It might also matter if the parents were legally divorced or not. If they were not divorced perhaps the legal custody is a non-issue. If they were divorced and the mother had legal custody perhaps an affidavit from her saying that she relinquished custody might help (I don't know, I am just throwing some thoughts).
On the other hand she could apply for naturalization in the worst case that she didn't meet all requirements for automatic citizenship.
I found this information on the Internet:
"In cases of adopted children, the INS will find that a citizen parent has legal custody "based on the existence of a final adoption decree." In cases of a child of divorced or legally separated parents, the INS will consider a citizen parent to have legal custody where the parent has been granted "an award of primary care, control, and maintenance" of the child by a court of law or other appropriate government entity. Where there is an award of "joint custody," the INS will consider both parents to have legal custody. In cases where the issue of custody is not explicitly addressed in a divorce decree or a separation agreement, the determination of legal or joint custody will be based on the laws of the state or country of residence. The regulations state that "[t]here may be other circumstances under which the Service will find the U.S. citizen parent to have legal custody for purposes of the CCA."
From:
http://www.nilc.org/immlawpolicy/natzcitzshp/nc035.htm