Dad comes off as a bully, in my opinion. It is not his ex-wife that is standing in the way of his relationship with his daughter; he's doing a fine job of driving that wedge on his own.

Having worked with a family therapist to resolve issues exactly like what OP is presenting, I can tell you that his approach is 180 degrees from what she recommended, and my daughter's individual therapist practically begged me not to force her into visits. Dad needs to accept that a visitation schedule that worked fine when she was nine isn't working anymore and he needs to reevaluate what is best for her.

If dad continues to insist that the only way through this is to strong-arm her into spending time at his house - and maybe he's got a court order to back that up - he needs to know that it is only going to cause resentment and sabotage his relationship with his daughter. Sure, he might succeed in breaking her and getting her to submit to the visitation schedule, which is all he seems to be worried about, but I don't doubt for a second that she will stop going the minute she has a choice. If he cares at all about his long-term relationship with her - beyond getting to her simply do what she's told - he's going to have to back off and acknowledge she's capable of making this decision for herself.

How exactly is the ex encouraging this? Because she got irate when she invited him into her home and he caused a scene when their daughter didn't do what he told her to do? I know I'd be pissed if my ex came into my house and took something belonging to our child and refused to give it back to her. He's got some nerve going into her house and throwing his weight around!

And the next morning he's still set on revenge - he was seriously considering going to the daughter's extra-curricular event and barring her from participating. He is nothing more than a schoolyard bully who when he doesn't get his way he grabs his toys and goes home.

Sorry, but OP is on the wrong path here.