Broody hen problem

[Berrie]

She has been brooding for about 3 weeks. I get her out each morning but she soon scuttles back in. We did make a broody coop and were going to get some hatching eggs until I read that as she is only young she will not be mature enough to raise a brood.
Anyway, thing is, one of the other hens picks on her relentlessly now and the other morning I found that she wasn't even sitting on the eggs. Could she be hiding instead?

Should I separate the bully into the broody coop for a bit do you think?

She might well be hiding, I've had birds do that. If you have several hens, then separating the bully for at least a week may change her place in the pecking order. But the new 'head girl' may just pick on the same hen.

Are they very young? The bullied hen may become more assertive as she gets older.

Getting a cockerel may not solve the problem either, we have one and our Amber Star hen still bullies the other girls.

Of course, she may still be broody or just coming out of it and in a few days she'll be out in the run as usual.

Last point, is the run big enough? Bullying is much worse when space is limited. Hens should be able to run away, failing that give them some 'one bird perches' as a place to escape too - upturned buckets or upright logs work well.

The run is 4x2m and there are places for her to perch out of the way. I let them out most days but even when the others are down the garden she still goes in!
Thanks for your help.