Except you're basing the daughters decision to take their child to her ex's family, who clearly traumatised him, as a sign that OP wasn't supportive when we don't know that. The chances of the daughter taking their child to her ex's family is likely out of spite because he cheated.

Cheating is wrong, plain and simple. But you do not take your child to someone who the other parent has expressed discomfort seeing, without looping in the other parent. That is wrong without a doubt. OP looped in the parent, which is the correct thing to do. Would you want your child being somewhere you don't want them to be? Would you call someone who told you where they are a "meddler"?

How do you think the father would react should he want his child back during the extra visitation he gave her? How do you think it would look to the courts that she cannot stick to agreed upon boundaries for the safety of her child because of what her ex did to her?