H.T.
My 4 year old daughter is the SAME WAY! She hates water in her face (ears, eyes, etc.) and it drives me crazy when it come to washing her hair at bath time too. What I usually try to do is have her tip her head way back and rinse her hair with a cup and just try to be careful not to get it in her ears too much. That way it doesn't go in her eyes either.
As far as taking her to the YMCA, this may be a good idea, but I think that forcing her to do something that she really doesn't want to do is going to make her dislike it even more. It may just be a stage that when she gets a little older and sees other children enjoying, she may just get over. I hope this helps. :)