Luckily most of the pools/beaches in my area understand that people need somewhere to train using swim-aids... the only bann I've heard of locally is the brand new State Swim center in Marion banning the wearing of cotton and velvet, t-shirts or streetclothes in the pools. The why there is completely understandable... such fabrics shed fibers in chlorine pools and clog the filters. So I wont be wearing a stretch velvet tail to there... That's okay.
My local pool even has scuba training lessons... so banning flippers seems kinda silly.

I think sometimes you have to weigh up whether the pool is a training/swim safety lessons pool or a purely recreational pool.
If it is the first then the rules need to be relaxed for swim aids, with the understanding that there are fully qualified lifeguards and swimtutors.
If it is the second, stricter rules for patron safety and less trained lifeguards might be more the norm.

From the sounds of it a lot of the banns/rules come from misconceptions via the safety risks of mermaiding... In which case, sitting down to calmly educate the boss/manager on the mechanics of mermaid tails and the Dolphin-Kick would be the best way to go.