Two things have worked for my swim team family. Your daughter will have to understand that if the chlorine roughs her hair, it will have to be detangled more and so she needs to cooperate with the program.
(1) Working coconut oil thoroughly through the hair before swimming. Another oil can work but I personally like coconut. In the summer when they are in the pool 2 times a day often, I would personally leave it oileduntil the summer ends, and keep it in neat braids. But my husband has a hangup about oiled hair, thinking it's "dirty."
(2) Wet hair or conditioner under a cap. My long haired daughter gets conditioner worked through her hair before a latex cap. (You can't put a silicon cap on conditioned hair -- it will fly right off.) I get the $1 bottles of conditioner from Suave sales, the dollar store, etc.
My short haired son does not like the conditioner and his hair is getting to the point where I don't just do the cap but I will have him saturate it in the shower and then put on a cap. When I use a silicon cap with him I will sometimes skip that step since most of his hair is pretty dry when the cap comes off. But, his hair is showing signs of damage so I am making him wet it now. I do work a little oil through his hair every week or so and try to leave it in. If it looks too "greasy" I can work some talc through it and make that go away without stripping. His hair is easier because if we don't like it we can always cut it off. DD would object if we did that.
We also do not use detergent shampoo very often as it strips. It's very rare for us to use shampoo. They usually don't need anything more than the above + a good shower rinse afterward.