It's great to see you here today at the Disney Parks Moms Panel, Joe!
The answer to your question is, yes, you can most definitely carry your purse with you on attractions. I use a full-sized backpack when I'm at Walt Disney World Resort and it fits safely by my feet or in another designated spot on every attraction. Even the more thrilling attractions, like
Rock 'n' Roller Coaster Starring Aerosmith or
The Twilight Zone Tower of Terror at
Disney's Hollywood Studios have enough space for you to keep your bag safely with you. There are even small pockets in the ride vehicles where you can put your smaller items like your hat or sunglasses. Make sure to check the pocket before you leave because items can sometimes get left behind in the excitement after riding an attraction.
If you get tired of carrying your purse partway through the day or you want to keep it in a safe spot and not have to worry about it while you're riding attractions, there are
locker rentals available at each of the four theme parks for you to stow away your bags and other items. Just collect your personal items when you're on your way out!
I hope this answers your question, Joe, and please let us know if there's anything else we can do to help you plan your magical vacation.
Jessica