Welcome to the forum, glad you joined. I'd guess from your screen name you are somewhere in Tennessee. Is that correct? That would give us an idea about the weather, especially in winter.
You might follow the link in my signature for some of my thoughts on room. While that 4 square feet per chicken with 10 in the run is not a bad starting point for a small backyard flock of all hens, there are just way too many variables for it to be right for everyone. Flock make-up, climate, how you manage them, your goals, whether you will add any later, and many more make a difference. I find the more I crowd them (and I sometimes do) the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with any issues that spring up.
Chickens do not know the difference in space in the coop versus space in the run. What is important is how much space they have when they need it, wherever it might be. The quality of that space can make a difference too. One idea on space related to chicken behaviors is that some just don't get along because of personalities and they need to avoid each other. That's some of them, not necessarily a lot of them, but the more they are shoehorned together the more likely they are to aggravate each other. Or they may become bored and start picking on each other. Many people get by fine with less than 4 square feet per chicken in a coop, but for some people it is not enough. I always want more rather than less, that generally reduces my stress levels when I have issues.
I really like the idea of a walk-in coop for anything over 8 or 10 chickens. That does not have to be on the ground, it can be elevated. You need to be able to reach every area inside even if it is covered with chicken poop for cleaning, repairs, or to retrieve an egg or a chicken that does not want to be retrieved. The bigger the coop the harder that is unless you can get inside. Then you need room inside to work. Do you ever plan to have more than 10 chickens?
I like the idea of a taller coop, that gives you enough vertical room to install your nests at whatever height above the bedding you want, then put the roosts higher than the nests so they don't sleep in the nests, then put your winter ventilation above any chicken sleeping on the roosts so winter breezes don't hit them on the roost. Slope the roof so rainwater runoff is not hitting you when you open the door or gather eggs.
In Tennessee yours should be able to leave the coop and go into the run practically every day of the year. That helps unless they are locked in the coop section only when they are awake in the morning. You may be OK anyway even if you are not up at the crack of dawn every day of the year to let them out. Or maybe you can install an electric door opener.
Attaching that dog house to the coop might help. Not for a certain square feet advantage but to give them a place to go to avoid each other if the door to the run is not open. If the run is available that's not necessary but the run may not always be available.
One thing I'd strongly suggest if you continue as planned is to put a gate between your new run and that dog pen that you can get through. With that horizontal you may need to get creative. That would tremendously increase the flexibility in managing them and that space. I really like flexibility.
I don't know if you are going to have any problems with what you are planning or not. A lot of people house them in spaces tighter than the general recommendations you see on this forum and do OK. Some have issues. Hopefully with what we've all written and by following that link in my signature you will have a better understanding of what you are seeing or what might happen and how you can maybe fix it if you have issues.
You might follow the link in my signature for some of my thoughts on room. While that 4 square feet per chicken with 10 in the run is not a bad starting point for a small backyard flock of all hens, there are just way too many variables for it to be right for everyone. Flock make-up, climate, how you manage them, your goals, whether you will add any later, and many more make a difference. I find the more I crowd them (and I sometimes do) the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with any issues that spring up.
Chickens do not know the difference in space in the coop versus space in the run. What is important is how much space they have when they need it, wherever it might be. The quality of that space can make a difference too. One idea on space related to chicken behaviors is that some just don't get along because of personalities and they need to avoid each other. That's some of them, not necessarily a lot of them, but the more they are shoehorned together the more likely they are to aggravate each other. Or they may become bored and start picking on each other. Many people get by fine with less than 4 square feet per chicken in a coop, but for some people it is not enough. I always want more rather than less, that generally reduces my stress levels when I have issues.
I really like the idea of a walk-in coop for anything over 8 or 10 chickens. That does not have to be on the ground, it can be elevated. You need to be able to reach every area inside even if it is covered with chicken poop for cleaning, repairs, or to retrieve an egg or a chicken that does not want to be retrieved. The bigger the coop the harder that is unless you can get inside. Then you need room inside to work. Do you ever plan to have more than 10 chickens?
I like the idea of a taller coop, that gives you enough vertical room to install your nests at whatever height above the bedding you want, then put the roosts higher than the nests so they don't sleep in the nests, then put your winter ventilation above any chicken sleeping on the roosts so winter breezes don't hit them on the roost. Slope the roof so rainwater runoff is not hitting you when you open the door or gather eggs.
In Tennessee yours should be able to leave the coop and go into the run practically every day of the year. That helps unless they are locked in the coop section only when they are awake in the morning. You may be OK anyway even if you are not up at the crack of dawn every day of the year to let them out. Or maybe you can install an electric door opener.
Attaching that dog house to the coop might help. Not for a certain square feet advantage but to give them a place to go to avoid each other if the door to the run is not open. If the run is available that's not necessary but the run may not always be available.
One thing I'd strongly suggest if you continue as planned is to put a gate between your new run and that dog pen that you can get through. With that horizontal you may need to get creative. That would tremendously increase the flexibility in managing them and that space. I really like flexibility.
I don't know if you are going to have any problems with what you are planning or not. A lot of people house them in spaces tighter than the general recommendations you see on this forum and do OK. Some have issues. Hopefully with what we've all written and by following that link in my signature you will have a better understanding of what you are seeing or what might happen and how you can maybe fix it if you have issues.
