There is one "family" restroom per park, at the Baby Care Center in each park. Those are designated for and meant for family use.
The other large single-room restrooms in WDW parks are companion restrooms for the disabled, which is why they are marked with a wheelchair symbol. While you certainly may use them, please be mindful that these are the only toilets (and I literally mean toilet, as in stool, not restroom) in each park that can be used by adult wheelchair users who cannot get out of their chairs unaided. With that in mind, please only use these restrooms when you really cannot manage in a conventional restroom, and please make it a point to finish up and get out of there as quickly as possible.
You might want to consider using a safety harness to contain a "runner" during restroom visits, or any other times when containing them in a stroller is not suitable and you will not have your hands free.