I'll start off by saying our swimming lesson journey was not a happy one but it does have a happy ending so I have a few ideas for you.

Most swim schools start doing child only lessons around this time however their "solution" is certainly not ideal and if you aren't comfortable with it then it certainly isn't going to work - remember you are paying them not the other way around. Insist that you sit beside the pool or get in with her and go through the motions with the swim teacher until she can trust the teacher again. If they aren't happy with this then certainly find a different school. We went through quite a few before we found one that worked with us. I'm not saying that our journey was without tears and struggles but it resulted in ahappy little boy who is quite confident in the water now