I don't have a lot of experience with broody hens myself, so I couldn't say if it's normal or not. I do know mamas of all species can stay attached to their babies long after they stop looking like babies, so if it was me I wouldn't worry about it too much unless you're concerned about a lack of eggs for your table. Your "chicks" on the other hand should be old enough now that they will start wanting some independence, and they may start roosting on their own soon whether mama roosts with them or not.
If the mama hen was showing signs of distress or illness, I'd be more concerned, but I think what you have is just a chicken case of a mother reluctant to kick her kids out of the house.