You have several different options but you do need to do something. If she cannot cover them all, you are not likely to get a good hatch. An egg that is pushed out will cool off. Maybe it will die or maybe the incubation will just be slowed a bunch. Then she tucks that one back under her and pushes out another one to die or get the incubation timing off. If one gets delayed too much, the hen will take the chicks that have hatched off the nest and abandon the unhatched ones even though they are viable. You usually get really lousy hatch rates if the hen cannot cover all the eggs.
You can put them all in the incubator and break her from being broody, you can leave her some and incubate some, or incubate them all and start a new batch under her. If you let her hatch some, you need to mark the ones you want her to hatch and check under her daily to remove any new ones.
Of course she gets irritated when you threaten her nest. She is really hopped up on hormones and very protective of her nest. You might want to wear long sleeves or gloves when you are checking under her. That does reduce the pain. But one of you needs to be the adult in this relationship and do what needs to be done.
I’m not without sympathy. When I was a kid one of my chores was to gather the eggs. When we had a broody I had to check under her every afternoon. Some of those broodies were mean! I didn’t have gloves and I didn’t want to check under them. But no way was I going to admit to my father that I was scared of a chicken.
