One thing to keep in mind is that POW is not a title that transfers on death - Charles gained the title 6 years after he became heir to the throne. So George may not immediately become Prince of Wales, but remain Prince George (formerly of Cambridge, formerly of Wales).
Taking QEII's children as an example, they would likely simply drop the "of Wales" and simply be Prince/Princess ___, and use Mountbatten-Windsor for passports or similar until they are granted titles upon marriage and become Prince Louis, Duke of Shropshire or the like. Charlotte will likely eventually be named Princess Royal unless they do some legal changes to make her eligible for a title in her own right.