Adding a different perspective here. Maybe this is a case of lopsided expectations due to comparing a gifted (or highly gifted) swimmer and your son, who sounds above average or more to me. Disclaimer: this analysis is based on what I've seen other kids do while watching my three taking lessons.
I haven't seen a lot of preschoolers who can swim laps and who have a "fierce kick," much less ones who are ready for a swim league. Most kids that age (even in the warm climate where I live) are working on getting in the pool or approximating the crawl for 15 feet. I wonder if your son's teacher is expecting your son to live up to the abilities of the other girl. (?)
I mean, goodness, he's five years old, which is a bit young to be focused on "work" in a pool. If the other girl enjoys it, great for her. But your son shouldn't be pressured into misery if he can't keep up and/or doesn't want to. He's just a little boy and this is supposed to be fun. And please ignore her mom; you don't have to organize your son's life to meet her needs.
Have you told the director direclty that your son is unhappy, that you think the teacher is part of the problem, and that you're thinking of leaving the class? It's wonderful that they created the class for him, but if the teacher is being too impatient with him, what's the point? If the director thinks the problem is exclusive to your son, yet he was able to work with the boy himself without the same problems (?), you might not have much luck getting anyone to meet you halfway.
I keep thinking, "He's a little boy!"
HTH,
Val
