I have custody of all my children( now mostly grown up) and my ex wife has a dismal attitude to them ( hating them because they are mine). Although I understand her motives, she really should have behaved better towards them as they were innocent of anything I may have done to her during our marriage. I didn't think she was fit to see them ( she used to describe our eldest son Danny who is deaf, as "not all there" or "retarded" which he's not) and never sent birthday, christmas cards or phoned. However I honestly thought that although this was appalling for the kids, they really were better served in having unlimited access if they wanted it, so I always encouraged them to call her, write to her, email her and visit her when we were in the area.
They made up their own minds fairly quickly and treat and consider my second wife to be their mother if anyone asks.
Upsetting as it was for them, it was also empowering and it fostered a very good relationship between myself and my sons and my second wife.
If I were you, I'd let him have unlimited access in however way pleases your daughter so that at least you've acknowledged your girl's wishes and allowed her to act upon them.She is in no way being disloyal and you need to allow her the freedom at this age to make her own mind up.