Hi Mandy,
Absolutely! You are welcome and encouraged to keep personal items with you on all rides at Walt Disney World, even the most daring ones. Bags and backpacks can be placed in restraining pockets in front of you or at your feet on all rides, including
Rock 'n' Roller Coaster, which does a couple of rollover loops.
I usually carry a medium sized cross-body bag and can keep it on while riding many
Walt Disney World attractions.
The one exception to consider: You are likely to get soaked on
Kali River Rapids at Animal Kingdom, much more so than on
Splash Mountain at Magic Kingdom. Because of that, free lockers are provided at the entrance to Kali River Rapids (on a first come basis) for you to store your bag if you don't want to risk getting it and its contents wet. I'm a bit of a wimp and also recommend wearing a poncho on Kali, too, by the way.
Thanks for visiting the Disney Parks Moms Panel. We're happy to answer all your planning questions to prepare you for a magical vacation. Enjoy!
Wilma