Bodyguards
No matter where the President goes, the secret service follows him and his family. If his children go somewhere without him, so does the secret service and the same rules apply to his wife as well. It can be nice to feel like you are always being protected at all times.
But we also think that this could be the worst thing ever when you just want to live your life and not be bothered by anyone. Imagine you are the daughter or son of the President and want to go out on a date. That must be a little bit embarrassing with a lack of privacy.