All really cool people are stubborn -- they're the ones who aren't pushed around by irrelevant things like other people's schedules and other people's priorities. Usually, in adults it's called determination, or character. In children it's only inconvenient because it reminds us that they're whole people with minds of their own.
I'm always really worried about those poor little passive children who keep waiting and hoping that some day it will be their turn to have a say in something, or that someday someone will 'just know' what it is they're lacking and give it to them. Just because they don't look needy doesn't mean they aren't.
Swimming lessons are for kids to learn to swim, right? If she's not learning, then the approach is not working for her, the method doesn't match her learning style or no one is respecting her need for things to go her pace or according to her curiosity. Yes, I know that this is an impossible task for a class setting -- but what's that got to do with your sweet little girl?
Yeah: nothing.
A class can't have her going at her pace, just as it can't go at the pace of every other child there. Some of those quiet children may be quietly being traumatized, while yours is fighting back instead. Who will ever know? They're too young to talk about it and much too young to have any awareness of it.
What can you do about it? Respect her clear communication and do what your intuition is clearly telling you to do. Your question states that quite directly, so I won't repeat it here. I know you know what you need to do, and I believe you will do what is best for your family. Do you know that, too?