Where are you located? What kind of outside temperatures are you talking about? Cold is usually not the problem but wind can be. That’s why they might need to be inside the coop, for wind protection when it is cold. If we knew how cold your coldest nights get we may be able to come up with suggestions or alternatives. Putting your general location in your signature can help a lot with this type of question.
I’m wondering if you can build something in the run to protect from wind when they are roosting until they mature enough to be able to roost with the older ones. My thoughts are either a hover or a separate but simple coop just for sleeping.
If you lock them in the coop section at night, they won’t be sleeping in the run. I found on another thread where you said your coop was 5’ x 6’. That is pretty tight for 13 birds, especially when you are integrating. 5’ x 6’ doesn’t give you a lot of room, but make sure they have plenty of roosting area, spread out enough that the older ones can’t bully the new ones on the roost. Like Aart, I use a separate roost, a little lower than the main roost, higher than the nests, and separated horizontally to give the younger ones a safe place to sleep that is not the nests. For three pullets you don’t need a lot but in a 5x6 coop you don’t have a lot.
They have been together for about a week and a half so they should be pretty well integrated. That means the older ones accept them as members of the flock and should not go out of their way to attack them. But they will have pecking order issues until they mature enough to force their way into the main flock, which should be somewhere around the time they start laying. Until then, the new ones will rank below the others. They will be afraid of the older ones for a good reason. If they invade the personal space of an older hen they are likely to get pecked. That’s why they sort of form a separate flock, they are avoiding the bullies as best they can. The exact same thing happens when a broody hen raises chicks in the flock. She will protect them until they are integrated but once they are weaned they go through the same pecking order issues. If you do decide to lock them in the coop section at night, I suggest you be down there to open that pop door before they wake up until you are confident there will not be a feathery mess. I do the same thing. It usually doesn’t take me long to get that comfort level. When I go down there after they wake up I usually find the younger ones on the roosts while the older are on the floor. The younger ones are avoiding the older by going up on the roosts.
While searching for your coop size, I saw where you are or were providing a solar powered light on a timer as it gets dark. That can help teach chickens to roost in the coop, but I suggest you turn that off and see if the older ones will go in on their own now. With that window you should not need it. I have observed that the younger chicks that are being integrated are usually the last ones to go in the coop. They are avoiding the bullies as long as they can. With that light on the bullies can see them better and may not have settled down as much as they need to. It will still probably take you a while to get the young ones to go in on their own but if you are consistent it can happen.
You should be able to manage this but don’t get any more chickens unless you build a much bigger facility. Please.
Good luck!