First, custody agreements can be changed. It sounds like you and DH could talk about it and do it without a lot of lawyers.
Second, my DH's kids stopped visiting as teenagers. We lived 4 hours away. It hurt my husband - but he knew it was more important for his kids a that stage in life to hang out with friends than spend at week with dad. Since we weren't too far away, he would try to make their games and catch a movie with them but not force them to spend a weekend or week away from what hey wanted to be doing. His kids visit more often now that they are grown. He gave them the freedom to make choices. Kids are only teenagers once, and it's a very important time for social development. They aren't robots.
I would ask her to compromise - a few weeks with her dad, the weeks of her choice.

OP, kudos to you and her dad for trying to figure out what is right.

DH had physical custody of his son who typically spent holidays and summers out of town with his mother. Once he hit high school it became tougher as he had part-time jobs and friends and things that made him less willing to go. Relationship between DH and his Ex was not amicable and so it was up to DS to explain to his mother that he no longer wanted to come for all of his vacations. I am sure it was hard on her, but he cut down his time away and went for a month each summer. I think it would have been even shorter but she wanted to take DS overseas to see her family and due to expenses and distances traveled it made sense to make the time with his mom more like 3 or 4wks.

Look---you are getting some peace for the summer. If she stays home, she will be a sullen mess at you AND your DH will be angry. Send her. She's way old enough to know that she doesn't always get to do what she wants to do.