Yes they do exist! I used to buy them from Etsy, but then I figured out how to make them as Etsy can be expensive sometimes. They sell non-slip grips at theribbonretreat.com. You can probably attach them to the hair clips you've already bought.
non-slip clips are great. My DD has really fine hair, and it seems like nothing stays. I just stick a bit of sticky back velcro on the inside of the clip. Works like a charm!
My LO doesn't have much hair, just enough to stick a little alligator clip bow in and I've recently found amazing ones at baby gap. They have a bunch of colors and the clip has little grippies on them so they stay in so much better and only for like 5-8$
Re: Hair clips that actually stay in
depends how much hair your dd has, but i order bows from etsy with nonslip clips:)
They are not perfect though, still slip around a little
I found the non slip non alligator clips work the best....order from etsy.
The best hair clips ever:
https://www.hairclippy.com/baby-toddler/