I use to teach swim lessons and was a lifeguard... 'green' hair happens to everyone but is easier to see with lighter hair colors or dyed hair.
As the below moms suggested plus some;
1) wet hair throughly with regular water (tap/shower water) before entering the pool
2) as soon as out of the pool rinse hair throughly and use clarifying shampoo that contains EDTA (Ethylene Diamine Tetra Acetic Acid) and wash your hair immediately after swimming
3) wash hair with tomato juice I believe the acidic nature of the tomatoes in the juice will gently strip the chlorine, leave in for a few mins then rinse out then do the typical shampoo & conditioner routine
4) There are products out there to help with this, you can go to your local salon and ask for a shampoo using that certain kind of shampoo that they carry to see it it actually works (go when the hair is green so you can see if it works, usually cost around $5 maybe a bit more depending on the prices at your salon). If the product works buy it, if you do not notice a change of green in the hair do not buy it, everyones hair is a bit different so one product may work for others and not for you.
I have heard of the baking soda paste but have never used it myself. Also I have heard of using lemon juice but that is very harsh on the hair and it could get the green out but it will damage hair if used too frequently (more then once a week is not recommended).
If it really is bothering you/daughter and none of the above works wear a swim cap while swimming.