Advice on female pigeon
Did you see the male pigeon do this? Maybe it's the heat, but I do not understand your reference to, "...when he pulls her down..." If you did not actually see the male do the damage, I think you need to look over the situation again. U shaped cut-Could there be another explanation as to what would cause this. Please post a picture.
It sounds like your female is not in breeding condition.
When this happens the male will keep chasing and pecking her head to force her back to the nest and keep her away from other males.
My advise to you is a follows.
Divide the nest box in half with chicken wire or other wire netting. Put the male in one half and the female in the other. Provide food and water for them both.
Keep them like this until the female is all healed up and feathers growing back on her head.
Its important they can still see each other through the wire mesh.. to keep them pair bonded.
You will know when she is ready to breed when you see them feeding each other through the wire mesh and see the female crouching down inviting the male to jump on her back.
Once you see this you can confidently remove the wire divider.
It may take some time.. and if you are worried about them being in the nest box all that time you can let them out one at a time to fly about and bath, exercise etc. BUT keep an eye on her that other males don't harass her in the main coop.
first you have a male that is driving a hen to the nest so has to lay. he may be to aggressive needs older hen the injured bird you say his mate has she laid before she is hand raised and may need to be introduced to him slowly and a second unmated cock is not good in the same pen with mated birds the hen needs to be at least 6 months old or older to start laying