Well, hello there, Marge! Thanks for rolling by planDisney.
I completely understand needing to haul ALL THE THINGS in the parks. My daughter and her twin brothers are 21 months apart, so there were many years that I was lugging bottles, diapers, toys, and clothes (so many extras!) with me on our park visits. I used our stroller to relieve my back many a time.
That being said,
Disneyland Parks' rules say that a rolling bag is not allowed in the parks. The rules include nothing on wheels pulled behind you, no large bags, and no stroller wagons. So, unfortunately, your rolling bag is a no-go.
But! Let's talk about ways to make your Disney day easier. If you have any bulky items you need access to but don't want to carry with you during the day,
lockers are available to rent. The lockers are in the Esplanade (the courtyard between the parks) and are located to the left of each park's entrance.
Multiple sizes are available, including a jumbo size, which can accommodate everything! Smaller lockers are also available to rent on Main Street, USA, in the Land and Buena Vista Street in California Adventure.
Marge, if the bag is for medical equipment, you can store medications in the
First Aid Centers in the parks. The staff will happily accommodate and grant access any time during park hours. If you have any other questions, please don't hesitate to reach out to us. I wish you a visit filled with pixie dust.
Rayna