I would strongly discourage them from moving unless they are staying for a long period of time and splitting the stay between 2, maybe
3, resorts.... they will see what a pain it is only afterwards to have to move so many times. Do they have cars with them? Are they aware that check out is 11 am and check in isn't until 3 pm, what will they do in that time frame? They will have to re pack and move luggage each time (the hotel will move it for them). It certainly isn't the most cost effective if they are on a meal plan that includes tickets because the more days your purchase your ticket for, the cheaper the ticket becomes per day. It also will become really confusing with meal plan credits. Credits don't expire until midnight the day of check out and then the guest would receive a new card at check in with new credits so it could be problematic keeping them all separated and making sure they use the right credits within the right time frame.
You personally can not call Disney and make any changes/notes to their reservation and you can not check in for them etc. at a resort unless your name is listed on the reservation. Disney will have the information in the system so no need to call and explain it to them. There shouldn't be an issues with extra magic hours because as long as they have a room key they are eligible... it's more the park ticket and meal plan credits that gets complicated.
Why are they switching rooms so much?
I know I sound like a Debbie Downer but after having worked on a room block for my own wedding guests and making sure everyone got where they needed to be I can tell you right now that you do not need the added stress of making sure everyone is checking in and out each day without problems etc.