If you and your ex both cooperate, this can be decided at your court date in mid-June and your kids could spend most of the summer with their dad.
Your lawyer could propose this to the judge, the judge could OK it on the spot, and it's a done deal. There is no guarantee of this happening, of course, but it is possible. I've been to court over my stepkids schedule several times and often the issue was resolved this quickly.
Also, at 14 & 16, most judges allow the kids to have a say in their parenting arrangement. Ours did. I would recommend talking with our attorney about that.
Your other option is, let them go to their dads for the summer. You CAN do this without a formal legal agreement. What that does is set a legal precedent for them spending summers with their dad, and this would likely be written in your updated agreement by the court. As you are in favor of this, I don't see why your lawyer isn't giving you this option.
This is why my ex and I did not use lawyers to create our parenting agreement, we used a mediator, and we adjust our schedule whenever we want - the courts are not in charge of our children, we parents are.
BTW - when my stepdaughter was 16, she waited until her mother went to work, then drove herself from Chicago to Minneapolis to live with us. Her mother protested, but the courts rubberstamped it. That's an example of why teenagers do get a say in their lives in family court.