the pool's solution is to have me in another room and her crying in the pool telling her "mummy will come back when you stop crying".
That is WRONG. When I was 5 a dentist said this to me but it was not my mum, my dad with me. I never forgot it. If I remembered the dentist name I would go let him know what I thought of him. I anyone ever tries this with my son they will quickly find out it is not on.

I would find another school or teacher, or put your foot down that if your daughter needs you that you are going to be there not in another room. Also spending time in the pool with your daughter outside lesson time might help.