Hermione could use magic outside of school because she wasn't entirely a hogwarts student. So she wasn't breaking any rules. Unless she used magic during the Summer after her first year.
Once she got a wand, she was bound by the reasonable restriction of under age sorcery, just like everyone else. She once even complained of not being able to do magic, because she cannot knit very well on her own, and so could make only two elf hats over the summer. With magic, she can make many more. Hermione could get away with some minor magic at the Burrow, because the Trace (which detects underage magic) can only tell WHAT spell was used around a minor, but not who cast it. If a minor casts a spell in an adult wizards home, the ministry must assume the adult wizard cast the spell, or else waste a lot of time prosecuting every spell parents may cast every day.
The Ministry relies on parents to enforce that law at home. And if parents don't enforce it, there is little the ministry can do, unless they personally witness it.