K.M.
Elite Aquatics in Lenexa is awesome. The place looks, well, don't be put off by the appearance! It's an older facility, but it's clean and the staff is really good with kids. The classes are limited to six and you get the same instructor for each class. The place is kept very warm and the pool is like bathwater!
I think it's expensive, but every budget is different. My daughter refused to put her head under water and they had her doing it at the first lesson. And laughing while she did it! She was never afraid again!
As my kids got older, we switched to the Blue Valley Aquatic center and they are good too. And less money, but I think you may have to be three to get in. You may want to look into that.
Sorry for the long-winded post! Good luck!