Hugs to you L.! You are definitely going through alot. Extended divorces are draining enough without adding in everything else.
Do you keep a calendar out to note family appointments, dad weekends, etc? If so, just mark the therapy times on there with everything else. When it's time to go, just load the kids into the car and go. If she flips out tell her she has no choice, you have to correct her vision and save her from potential bigger problems caused by not correcting it. Whether she's embarrassed or just upset cause she wants to go play with her friends, she needs to go. Let her know that if she does her exercises religiously, the therapy will be over much quicker, and not drag out for years and years.
Yes, you could just correct the farsightedness and ignore the double vision, but that will add to future problems, especially in the reading department...so that will affect all her schooling and even future careers. You have the opportunity to correct it, and should. My son had to do several different exercises daily, including one they called eye pushups. They literally made him ill the first week or so, which you can imagine did not make him want to do them. But we pushed through it and were done in under a year. He still goes to a weekly tutoring program to help with other issues like crossing midline, and after 5 years, it is getting old for him (and me). But hey, that's what we moms do!
I'm sure dad is doing his best to just be Mr. Good Time Charlie. He wants to be the popular one, so he's not going to push the issue with her. If you have to do it on your own, you just have to be more clever, and find ways to submarine his efforts which are not helping your daughter. If it helps, say you'll pick up a friend or two to bring back to your place.
Hang in there L.! And good luck with your divorce.