Twinkie could she be upset because most of the time there is a confrontation between you and ex dh.Children feel torn when parents split and she is obviously not coping very well with the situation.
can someone else drop/pick her up, that way your dd will not see the confrontations you have. Surely your dp or a friend or even your uncle could do this for you and your dd.
Try it for a few weeks and see how it goes.
The letter to his mother go for it, you have nothing to lose.
As for the bashing thing (ok you cant see him doing it) is there any bruises/ marks on her to substantiate this remark.
If there is why arent you keeping her with you END OF.You see I dont understand this as what is the worst that could happen if you KEPT her and reported this.You only have your childs best interests at heart so I cant see any authority body ie social services/ police sending her back there with those allegations.They would have to investigate these claims and she would not go back until they are satisfied.
On the other hand if she is not getting bashed it seems to me she is playing the both of you off against eachother.She knows how you both tick and what will get you both angry.