I'll chime in with the same advice-- we bought 2 weeks of swim lessons for our son, and while he loves the water by himself, he did not like the swimming lessons. We stuck to it & let him go at his own pace-- mostly playing with the teacher-- him outside the pool, her inside, and she would coax him to put his legs in, go up to his tummy, etc. We practiced at home, since he wasn't making much progress at the lesson, but dealing with a stranger every day seemed to make him trust me more & he wound up walking on the bottom of the pool with me (he's 5). Then, at the lesson, I would stay by the side & he would go in with her but walk to me.
In a nutshell: stay close & be involved, try to generalize the pool from the swimming lessons with the teacher to just playing around with you & she'll get there eventually.
My son still isn't swimming but he is way more comfortable.