Your daughter is old enough to know what she wants and doesn't want. The sad part is, she doesn't want her Daddy. The sadder part is....Daddy can't seem to make her understand how much he loves her. What does that mean? Does that mean she's just more "secure" with Mommy? Does that mean that Daddy is verbally abusive to her, too? I don't know what it means actually, but her actions & emotions aren't lying.
In my opinion, if Daddy wants to be a GOOD Daddy, and "earn" her trust and security, then he should be staying at your house, as she asks. Once she's relaxed enogh in her own home to be with him "safely", then perhaps she'll be brave enough to want to go to the Zoo, or his house, which could be called her "other house", or wherever else outside of your home.
Tell your Ex that you don't want her to go through this anymore, and that you "feel bad" for him having to stand there waiting for her to go with him. Tell him for a couple of weeks, let's try to have him stay over at your house in HER comfort zone for regular 1 hour visits. Then go from there.
If he won't do that, then you will have to "prepare" your daughter for visits with Daddy. Doing so about 1 hour before Daddy gets there will hopefully help her in the moment it's time to go. Even though you KNOW your Ex, and probably don't want to say nice things about him, you will HAVE to for your daughter's sake. Daddy loves her. And by saying things like, "Daddy's coming to over so you can visit his house....you're so lucky!"....or whatever :O)
O., I hope something in my opinion can help you through such an emotional time. It was hard for me to "look past" the part where "he left when she was 4 months old"............and still try to give him a decent chance for a relationship with his daughter.