Hello Khadijah!
Welcome to planDisney! Oh boy, you are gearing up for an adventure next year with your little ones!
According to the
Walt Disney World Resort Property Rules, "any trailer-like object that is pushed, pulled or towed by an Electric Conveyance Vehicle, wheelchair, stroller or person" is prohibited. This means that a buggy board, stroller board, glider or any other similar attachments to your stroller will not be allowed. In addition,
strollers cannot be larger than 31" (79 cm) in width and 52"(132 cm) in length.
I have been going mad for a bit trying to think of a good solution for you. A search for a Disney sherpa resulted in some nice outerwear- not a person with excellent trekking skills who can provide parental support. (Darn) As a mom who has had to wrangle her kids alone quite a few times, I especially relate to your struggle. A stroller is an absolute must when in the Parks and with how young your children are it is the smart choice to have one with you. Due to the stroller sizing rules, you are limited in your choices. There are only a few triple strollers out there that will be allowed. My research has found a few options after I searched "Disney approved triple stroller" in my favorite search engine. I found that the Joovy Qool Triple Stroller and Zoey The Trio triple stroller fit the sizing guidelines! I don't know if any local Orlando stroller rental agencies can provide them but maybe there are local moms group of triplets or young children that may be able to assist you. I would also consider bringing the stroller you use at home if it fits as well or investing in one that you like. Remember, stroller wagons are not allowed even though they are fabulous transport tools for children. Maybe having one from home would make traveling from Great Britain much easier. You would have a place to hold the tired little ones while maneuvering around the airport and if you're smart a cupholder for mom to hold her drinks.
Another option that could work if you have children who are willing to squeeze in a bit and share space peacefully (miracles do happen) is to
rent a double stroller from Walt Disney World. These strollers are designed to be like large bench seats and I have squeezed in desperate situations three little kids across the row. The only issue is that it cannot leave the Parks and must be returned each day. This means there is a chance you will have three little kids who are falling asleep to wrangle from the Park exit to your chosen transportation method. Not ideal but something to consider. Maybe, plan for shorter Park days with nice pool and rest breaks in between to keep energy and moods elevated. Don't forget to bring snacks! One of my favorite summertime tools to keep kids happy in the Parks are portable mini fans for each child and insulated water bottles that keep beverages ice cold.
I'm sorry that I didn't have the answer you may have wanted but I can sense that you are a tough and wise mom who will make the best choice!
Let me know if you have any more questions!
Happy Planning!
-Nimmy