Mira has been going for swimming lessons since she was 1. here in Singapore the instructors are alll AusSwim too. It's so gradual, the way they teach. and it's all about repetition. Mira is happy jumping into a big pool, she can go under and kicks hard to get to us, she can probably swim a meter which is huge progress.
Marissa's mama - your daugher is still very young I'd be wary of putting too much pressure on her. The more she senses you being sad (as you put it) and the more upset you get because she won't let go of you, the more she's going to dread swimming because mummy gets sad. So I'd really give it a rest for a bit, go back to just having fun in the water. And when she sees how fun it is and how happy mummy and daddy are, she will feel less pressured. I have no doubt that she will be swimming like a fish one day, but you don't want to instill any fears in her now as it will take longer to break as she gets older. Just make swimming fun. Bring in loads of toys, like rubber toys that can squirt water. Teach her to blow bubbles, she'll find it funny. And, one thing they teach Mira is "monkey hands". This is where they hold on to the side, and will hand walk over to the ladder. You can put a toy she likes about a meter away, and assist her in monkey walking to the toy. Mira now does the whole pool by herself and she's so speedy. I really truly believe that it's all about fun - and of course safety. But a kid needs to feel safe and happy in the pool. HTH