A.M.
i kind of agree with DVMMOM. she is six, not three. in your situation, if it was me, i would be putting my foot down and having a grownup talk with her. she is a big girl and either she wants to swim or she doesn't. period. if she wants to but is nervous, that is okay - but being brave means doing something even if you're scared. if she really wants to do it maybe the two of you could work on a strategy for making it easier on her. but in the end she needs to make a decision and stop the tantrums, because that's what these are. a little compassion is fine, but at this point i would be getting firm. if as you say it's getting disruptive, then it needs to stop. one way or another.
********
ETA: J., i had the following conversation with my 5 (almost 6) year old this morning. he started swim lessons today. he has finally gotten (just this year) to where he's not scared of swimming in general - but he still hates putting his head under, and won't jump in to me at all.
son: "mom i just don't WANT to go to swim lessons!"
me: "well let's talk about it, why don't you want to go? are you nervous?"
son: "yeah i just don't want to put my head under water."
me: "oh that's okay. hey if you don't want to put your head under water, you just tell them, 'i'm not ready to do that yet.' then you don't have to. you only do what you're comfortable with, ok?"
son: "okay!"
me: "it's totally okay to be nervous about something, but we still have to go. being brave means doing something even if we're scared. i bet by the time swim lessons are over YOU will decide that you want to try putting your head under water! but it will be when YOU decide, ok?"
end of problem. and it was so sweet - he goes to daycare while i am at work, and that is who is taking him to the swim lessons (great set up!). as soon as we walked in this morning, he walked right up to his teacher and said, "i'm just not ready to put my head under the water yet." i was so proud of him lol.
a lot of times i am so tickled, it just seems like when he can articulate what is wrong, it helps him SO much. it helps when he knows i support him no matter what, and it's okay to FEEL the way he does. but he also knows there are certain things he still is expected to do.
hth!