I read that White Leghorns aren't good mothers, so I will probably have to incubate. Either that, or get another breed that are good mothers, and have them take that responsibility if possible. Otherwise, incubate.
You could consider getting some bantams to do the incubating.
I've had some Old English Game bantams that were good mothers.
They can live with any of the other flocks except when they are sitting & raising chicks.
A hen doesn't care who laid the eggs she is sitting on. So as long as you can tell which eggs were laid by the hens you want chicks from, you can just put the right eggs under the broodies.
I guess the plan would be to use the males as meat chickens, but can you really have a bunch of males running around in the same coop?
How long do you think you are going to be raising these males before you butcher them?
If you want the meat nice and tender, you have to butcher them fairly young (maybe 2-3 months).
For almost any of the common breeds of chicken, males live together just fine up to any reasonable butchering age, and usually well past that point.
Ones that were specifically bred for cockfighting might have issues, but you are not talking about having any of those.
If I have one coop with 15 hens and 1 rooster, another coop with 15 hens and 1 rooster (they say for White Leghorns, up to 15 hens per rooster), would I use the same 2 roosters to make more chicks? Meaning, would I take one of the rooster out and put him in the spare coop and throw in a couple hens and make some babies? Or should I have a rooster(s) that are specifically for making babies set aside in another coop...maybe one of the meat chickens? Just trying to think through the process.
If the rooster is in the pen with the hens, he will mate with them.
After he mates with a hen, every egg she lays for the next week or so will be fertile. She might keep laying fertile eggs for two or three weeks (some do, some don't).
If the rooster had 100 hens, he probably would not mate often enough with each one, so some would lay infertile eggs-- that's where the advice about how many hens per rooster comes from. With 15 hens per rooster, he will probably do just fine with all of them.
When you want to hatch eggs, you do not need to move any chickens to other pens. Just collect the right number of eggs, and put them in an incubator or under a broody hen.
When you do not want to hatch eggs, collect eggs every day and store & use them like normal eggs. Fertile eggs will not develop chicks in the refrigerator, and they will not develop chicks if you store them at room temperature (unless your room temperaure is as warm as an incubator.)
If you do not want to hatch chicks, you do not need a rooster at all. Hens will lay eggs just as well if there is no rooster present. Having a rooster is not a problem, but it is also not needed.
For hatching the eggs, a broody hen is content to be a single parent. She does not need the rooster around to help as she sits on the eggs and raises the chicks.