Question: Broody Hen

I am hoping some of you have some answers for a new chicken raiser!

When we bought our chicks last spring, we chose breeds known for being good mothers in hopes of having some success in raising our own chicks.

This week one of our hens has taken over a nesting box. I've never seen a chicken sit like her. She is completely flattened herself against the nesting box floor. Is this a sign of being broody?

Our hens are quite tame and if one is in the nesting box when I check the eggs, I just lift them up to peer underneath to check for eggs. Usually they take the hint and jump out.

This one is different. She isn't mean and doesn't peck but she also doesn't move. I slide my hand under her, take her eggs and she just sits there and glares at me.

Maybe it is mean to take her eggs. I'm not sure what to do. If she is going to sit on eggs, I'd like to give her enough eggs to make it worth her while that would all begin incubating at the same time.
Should we move her to a new spot where she isn't disturbed by all the other hens and rooster? Or would moving her to an unfamiliar spot, even in the same building, confuse her?

I welcome any advice, personal experiences, or ideas! Thanks!