We have thin hair around here, different type of problem, but i saw this website awhile back and thought i might suggest it.
"Our products are patent-pending and unique. We fully wrap each hair clip in the highest-quality Swiss Velvet, so it’s soft against your daughter’s head, and tuck a small, safe magnet under the velvet for a secure clasp.
Our baby bows® are beautifully
hand-crafted, and guaranteed not to slip or slide in even a few strands of delicate hair."
To be honest though, If I were you, I would gather her "bangs" and sides and pull them up to a half pony tail on the top and use no pull elastics maybe even adult ones (like Goody) if she has enough hair. You could always add a cute clip on the sides or near the elastics. Wish i could show you a picture i'm not sure that makes sense, it' sounds like she has enough hair that it wouldn't look like Pebbles Flinstone, but flow down her back instead.
My SIL introduced me to decorating my own hairclips with differents ribbons and i'm totally addicted now, It's lots of fun, i may try the magnet idea on the clips i make for my daughter.
Enjoy your little girl, I hope you find something that works