WW wants to maintain friendship with AP

I am a month post DDay. WW had an EA with AP, who is our children's PE teacher and also coaches at her gym. They act like acquaintances in front of others, but were constantly messaging over IG, Whatsapp, and various other apps. I have accepted that it is not fair to the children to move schools because of the EA, and my wife has a lot of other friends at the same gym who she does not want to lose. However, I have asked that she keeps it strictly professional - she is not to message AP unless it is related to school or gym.

She has stopped with the DMs and private messages, but is still chatting with AP over group chats. The problem with some of these chats are that there are only 3 people, and the 3rd person (presumably a mutual friend) has not contributed to the discussion, or responds once a week. The topics are also not what I would consider professional, such as sharing memes, or gossip.

AITA for insisting she maintains that professional boundary with AP, or is friendship with the AP allowed?

Update: I have made known to WW that I am uncomfortable with the group chats, and she will no longer participate in the gym ones. She will reschedule to other sessions where AP is not the coach. She'll also be adding me to the school-based chats. I have made my feelings known, and she has obliged. Together, we have looked for solutions that I am OK with. Don't think I can ask for any more than that.