First off, best option is to find TURNOUT for these horses. It's no wonder so many of them are aggressive and angry if they are stalled 24/7, and if a lot of them are youngsters, it's going to seriously screw them up for the rest of their lives, both with people and other horses.
I know it's not your decision, but it needed to be said.
Secondly, bring them outside. Surely there must be an arena or something they can have a run around in for just a short time? You could also build up to turning them out in small groups so they at least get SOME social interaction?
We regualrly muck out our stalls with the horses in them, but this is only because they are all quite happy for us to do this. I would never do it with a particularly young horse, one that was nervous when stabled or one I didn't quite trust.
If you have had lots of practice mucking there is no reason to remove the horse to clean their stalls. Any horse, any age can be taught to stand where you want them while you clean their stall. Yes, it takes time and patience but they should all be taught to stand against the wall and remain there while you muck. During the first few days of life our mares and foals are mucked out while still in the barn - I use a muck tub in the stall with the door closed and then transfer the contents of the but to my wheelbarrow. After picking the stall out several times a day the foal quickly gets used to the program. Before long I can clean out the stall just the wheelbarrow blocking the exit. Even then I always keep myself between the horse and the exit.
I think you should be able to go into a horses stall with the horse and do anything safely. He should have manners!
That being said. I prefer to put mine out to clean. I have 2 that I 100% trust, I even have one that will lift his feet one at a time for me to get underneath them. I have a 2 year old that is actually very well mannered but I'm careful around him because he is a baby. I have a mare that has never done anything in anyway but there is just something about her that has always got me paying closer attention around her.
I think it's easier to clean with them out of the way, you can do a better job and you don't have to keep your gaurd up. I also think horses should be turned out for as many hours as possible in a day. I hate that those horses are stalled 24/7, especially as babies.... very sad...
I agree its tough with horses being stalled 24/7. They are naturally going to be more nervous and nasty. I don't stall mine but they are kept in a 2 acre dry lot all winter that has to be cleaned out weekly or the poo gets deep. I use motor equipment (tractor etc.) to do it. I tried doing it with the horses in, but they get curious and won't stay out of the way. I put them in the round pen now till I'm done. I can't imagine doing it (quickly anyway) in a small stall with the horse in it.
I was always taught to take the horse out before you clean. No matter the state of the horse, whether it be calm or spazzy, I'd take the horse out. Wouldnt it feel nice to be out of your box for that small amount of time anyway?
I think it really depends on the situation. Generally speaking I think it would be hard to do a good job cleaning a stall if the horse is still in it. If I had to be put in that situation, I would move the horse over to an adjacent stall while I'm cleaning and just put back when you are done.