Surely if your DH has the kids 50% of the time (I'm assuming he doesn't have less than that because you clearly think he's the better parent, so he must be doing the minimum of an equal share in parenting) then he takes the kids to the open days on his time with them, he uses his parental rights to get the kids to take 11+ exams/entrance exams and then, depending on the results, the DC decide where they want to go.
If she "stops all contact" you go back to court and get it reinstated.
He'll probably need to do tutoring/practice papers with them as well, as many of the grammar school entrance exams use Y6 questions, but at the start of the Y6 yr, when they probably haven't been taught to that level yet.
If your DH wants his kids to go to grammar school, then let him handle the necessary education, exams and entrance paperwork etc. Their mum can do the relevant work for the local comp.
I'm not sure why this is an issue 🤷♀️
Unless he's leaving his ex to do the bulk of the parenting, education and homework etc and only sees his kids EOW or similar but expects her to do the heavy lifting of open days and exam prep etc for a school she's not bothered about them going to; is that the case?