Dmitris:
Because Disney buses require that you take the children out of strollers and fold them up, my best recommendation is to encourage you to stay at a Disney resort that is on the monorail or boat. If you think you'll mostly visit Magic Kingdom, consider looking at the
Contemporary Resort so that you can keep them strapped in from the park to the monorail to the elevator to your room as the monorail stops inside this resort. If you are staying near Epcot and Hollywood Studios, you will be able to keep the children strapped into the strollers if you use the boat launches. The resorts in this area are Beach Club, Boardwalk and Yacht Club.
If you are on a budget and the deluxe resorts seem out of reach, look at
Wilderness Lodge which takes a boat to the Magic Kingdom or the
Swan Hotel which is near the Boardwalk and uses a boat for transportation to Epcot and Hollywood Studios.
Wishing y'all a magical vacation!
Whitney