Hi Susie and welcome to the Forum.
I have only hatched quail chicks in an incubator and if you have successfully got a pair to breed, you have done very well as this is quite rare. Mostly they don't sit on eggs or go broody very often, or they give up part way through. So I have no experience of allowing hens to raise their own chicks to maturity, or trying to introduce youngsters to an older established group. However, I had tremendous problems with injuries to the young hens at about 6-8 weeks old, when the males were just coming into sexual maturity and finding out what it was like to be a teenage boy. I got to the stage of dreading whether I would find yet another bloodbath in the cage when I went down in the morning! I don't think this was bullying as such, just injuries mostly to the head where the male had gripped the female when mating and hung on when the thrown off sideways by an unwilling partner, thus tearing off a chunk of skin. Not the sort of injuries resulting from one male bird attacking another. Is this your problem? I did try to sex them, but didn't find this very easy, and like you, I had a couple of males that I was fairly sure were female until they seemed to suddenly change sex overnight and have a go at the girls! Out of the 17 I hatched, I ended up with 11 boys, which didn't help. In the end I took the difficult decision to cull all the boys, and after this the girls lived happily and productively together, they are now 2 and a half years old and still laying prolifically.
I suppose that if you are trying to introduce young males to a pen with an older cock, trouble is likely as the father bird will see them as rivals. Wild quail would disperse at this stage, or a least even in a flock wold have all the space needed to keep clear of more dominant rivals. I think that, with any kind of poultry, its always a problem to know what to do with the boys. You may find that they will live with each other OK in a bachelor group, especially over the winter when not in breeding condition anyway, but you may have to cull them eventually I'm afraid. Trouble is, they are best in a small group of about 4 females to one male, so the females don't get over mated, but inevitably this leads to a surplus of males. My experience of hatching far more boys than girls is apparently not unusual for quail.
The other thing is that quail always take a very long time to adapt to changes in their social group, where this means introducing new birds, so this can be difficult too. You could try what chicken keepers usually do, and split the cage with a wire barrier so the two groups can get to see and know each other through the wire for a week or two - with any poultry, if you just plonk new birds into an established flock without careful introductions, there will be trouble!
I wold be interested to know whether the aggression you report is actually male-on-male, or mating injuries from teenage males on young hens, as evidently these are different problems.