Hiya Ellen!
I recommend sturdy walking sandals for your little ones that preferably strap to their feet so that they don't have to worry about the sandals flying off.
Check to make sure they don't rub too much in any one spot, but bring bandages and mole skin just in case.
I usually bring 2 to 3 pairs of shoes for the kids to avoid blisters forming...walking sandals, birkenstock sandals/slide sandals, and sneakers with socks. By the end of our trip, my kids are usually wearing nothing but sneakers and socks for the comfort.
The only ride that I can think of where you need to worry about removing sandals is Soarin'. If you or the kids are wearing slide sandals or flip flops take those off and stash them in the storage space under the seat during the ride...you'll understand why once it starts! Other than Soarin', I would encourage the little ones to keep the shoes on in Disney World!
Your trip is almost here! I hope that you have a magical time in Disney World!