My question is: Should visitation with the father be left up to the discretion of the child? In other words, if she does not want to visit, should that be the way it is, or should that be something considered but ignored with visitation taking place anyway?
What would be in the best interest of the child?
Of course the child should not be guilted or coerced into visiting her dad, anymore than she should be made to feel guilty if she does visit him. In an ideal world, your boyfriend and his ex would be able to sit down and have a dialogue, wherein feelings on both sides are expressed and the focus is on how their daughter can maintain the healthiest, most loving relationship with both parents. In the usual world of bitter divorce this dialogue can't take place because the parents won't put aside their own anger and egos to focus on what's best for the child.
I would hope if they can't have the ideal dialogue that I described, that they (ex husband and wife only) seek out a skilled family therapist who can mediate a child-centered dialogue on this issue. The daughter has got to be taken out of her untenable position of having to hurt one or the other parent. I hope they can focus on "the prize", their child. You can support your boyfriend and encourage him to "do the right thing" but clearly need to absent yourself from playing any active role with the mom or the daughter; this is their family dilemma.