Welcome back to planDisney, Loretta. Thanks for giving us the chance to help!
Are you familiar with the
Property Rules that are in place for Walt Disney World Resort? I would recommend thoroughly reading through these guidelines to determine whether or not the push cart you'd like to bring will be permitted. You don't specify the exact dimensions of your cart, but there is a rule that might apply to the item in question. The rule I'm referencing states that "trailer-like" objects that are pushed, pulled or towed, whether by an electric conveyance vehicle, wheelchair, stroller or person are not allowed. I'm concerned that the push cart you're inquiring about may fall into that category.
Would it be possible to place the backup equipment your daughter needs in a backpack and hang it from the wheelchair handles? I've seen several Guests utilize that method of hauling personal belongings in and through the theme parks.
Another option would be to store your belongings in a locker while you tour the parks. Doing so would allow you to access the items when they are needed. Each of the theme parks and water parks have
keyless lockers available for rent on a first-come, first-served basis.
I hope that helps, Loretta. And I'm wishing your and your family an unforgettable vacation!