You need separate coop/run set up to keep 3 roosters in. Or you could put one rooster with the hens and have a separate place for the other two.
Truthfully, I would highly expect this to go poorly. It just very seldom works with the setup you are describing. Most people do not really believe how badly it can get. Rooster behavior today is really no indicator how they will act tomorrow.
I know you want to keep them, and are wishing they will all just get along, and will probably try to keep them. My advice to you is to have a alternative plan SET UP and ready, and a way to separate either fighting roosters, or roosters attacking the hens. A chicken hook or a fishnet is very handy to do so. Wear leather gloves, and a long sleeve shirt. Have a cage or crate set up and ready to go.
Good luck, but I have had chickens for years, and would not expect this to work well for either the hens or most of the roosters. They don't call it cock fighting for nothing.
Separating them at night won’t really do much. If they have access to each other the boys will hurt the hens and each other. Multiple roosters can live in the same flock fine, but not with that few hens. They either need way more or none at all.