Before she will even consider learning to swim ... she is going to have to have the desire herself. Simply because you want her to overcome her fears, she likely won't. She needs to be motivated herself first. She needs to want to over come the fears. I feel the fear of the water is completely normal and reasonable. I was about to take lessons then had an almost drowning experience. For about 2 years after that day I had no interest in learning to swim at all. Eventually the desire to learn returned and I took lessons. About the same time I "found" TI. Without that discovery, I doubt I would even learned to swim. The lessons were useless and I ended up being self taught by following TI and spent hours with lots of patient, progressive practice. Something new learned with every swim. And this was motivation to keep coming back for another try.
So as an analogy ..... her desire to learn must be from within. People who want to quit smoking need to want to, from within. All the coaxing will never make them stop. So don't coax her .... "because she should learn" .... let her see the enjoyment that can be had if able to swim.
If you're not swimming; then you should be skiing......