My advice is in line with the others. Each chicken has its own personality. Each flock has its own dynamics. We keep them in so many different situations and circumstances that no one answer for something like this can be right for everyone. I do think how much room they have has a lot to do with success, the more room the better. With a bit of room, two roosters and 13 hens should be fine.
I always suggest you keep as few roosters as you can and still meet your goals. It’s not that you are guaranteed more problems with more roosters, just that you are less likely to have problems with fewer roosters.
Two or more roosters will decide which one is dominant. Sometimes that can result if pretty vicious fights. Sometimes unless you’re really paying attention you won’t even notice. Usually it involves a fairly minor skirmish that is over pretty quickly. With them growing up in a flock, either as brother-brother or father-son, it often goes fairly smoothly but do be prepared for some skirmishing, chasing, and running away. That’s where the extra space comes in. The loser needs room to run away and get away.
With two roosters and 13 hens you will probably see the flock split with each rooster having his own harem, especially if they have room. Even with that, it is also possible some hens will form their own third flock, hanging out together away from both roosters. They are living animals with their own personality. You really can’t tell for sure what will happen.
It is certainly possible with many roosters and especially with little space that some hens can be overmated. But it is also possible with one rooster with perfect technique and 20 hens for some hens to have a bare back. Some hens just have real brittle feathers. Through no fault of the rooster their feathers are going to break and they are going to be barebacked. It’s not always the rooster’s fault, but that’s one of the reasons I suggest you keep as few as you can and still meet your goals. Two roosters with 13 hens sounds like a very reasonable goal to me but due to your unique circumstances it may not work. Good luck!