Honest answer? move the classes to the weekdays, you should not dictate what the other parent do with his contact time.
I have seen such a formidable fallout of a divorced couple, after years of both parents being forced to take children to classes during each other time without the agreement of the other parent.
Whatever the children were getting out of the classes was NEVER enough to justify living in the middle of constant animosity, aggressiveness and ultimately pure hate between the parents, most of it stemming from the constant argument about extra curricular activities.
Just think the things the other way around... you have your child only once every other weekend, you want to take them to the park, for a walk, to visit family away of the city or just enjoy a day out with the family... but you can't, because that time is not really yours, it is already compromised with activities.
And yes, a judge would rule for the activities to continue.. or not. It all depends on the case, how well each solicitor presents their case, the judge itself, and the position of the moon. That is the thing with English family law, there is nothing written in stone (or in paper for that matter).
However, I think there is one thing most judges would agree with: the parent that blocks contact is the one who is perceived as the aggressor that needs to be brought in line (or the badie, in more plain terms).