Firstly i think it is disgraceful the way that she spoke with you.. massive
Personally i haven't had to deal with it and yes i can see that there may be 'challenges' in providing care for a child with a disability or physical impairment but that does not mean they cannot make suggestions to accomodate you.
At the very least she could have said i'm sorry our policy is ........ but if you'd like to speak to a manager.
I am assuming like most leisure centres it is an every day staff member 'babysitting' and she's not wanting to do the extra work as she's not properly trained to be a carer.

Hoping the centre has the decency to respond, if not i would be taking it as high as possible just for their lack of empathy.