You need a lawyer to answer this question; like yesterday, because they might not wait to go after you and take you down.
What was the general attitude, tone, reasoning? That should have given you a good feel for where you are.
My first guess it that they believe the charity link and the picture are being used in a context that could imply an endorsement. That could be a big problem. It makes me wonder that if the charity link were not there, and the picture were clearly captioned as, "This is my daughter with Fighter X.", if anything would have ever been said.
If it were me, I would take one of several courses:
1) Comply immediately.
2) Bring in an internet attorney immediately.
3) Comply within reason immediately, and show that you don't want to step on any toes, but that you are claiming that they are overstepping in the full extent of the demands.
4) Whatever you do - don't wait a moment.