2 to 4 in the coop? I’ve seen anything from 1 to 16 square feet per chicken is needed in the coop on this forum. There are a lot of variables involved so there is a wide range of numbers that actually work, but 1 and 16 are both pretty extreme. Even most commercial operations don’t go to 1 square feet per chicken.
You might follow the link in my signature below to get some of my thoughts. A lot of that won’t apply to you but some will and you might get some management ideas out of it. Or maybe more questions.
From what I read I suggest you start with maybe 4, no more than 5 hens. They should lay a lot of eggs for you. They will not lay year round. Depending on what time of year they are hatched and eventually start to lay, some pullets will lay through their first winter and on until the next fall, but some don’t. In the fall hens normally molt when the days get shorter. They replace their feathers and stop laying, using the nutrients that were going into egg production to grow new feathers instead.
I find the more I squeeze them the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with issues that do come up. Chickens poop a lot. Poop management may be a good chore for your kids. But the more chickens you have pooping in a small area the more you have to manage the poop. That’s an example of having to work harder if you crowd them.
I spent a year in Houston after Katrina. Cold is not your enemy, heat is. You don’t need much of a coop, mainly something to protect form rain and strong winds. What you do need is plenty of shade and great ventilation in the heat of summer.
Most building materials come in 4’ and 8’ dimensions when you buy new. I don’t know how you plan on setting that area up but you might consider a 4’ wide coop. You might get less cutting and less waste of materials plus a larger coop for no more money.