Sounds normal. I've had broody hens cut them loose at three weeks, others not until they are almost 3 months old. Once she weans them, they are on their own with the flock.
My flock, coop, and run are all significantly larger than yours so that can change a few things. Typically the chicks learn to avoid the other adults while Mama is still raising them. If they invade the personal space of another adult they might get pecked or chased so they quickly learn to stay away. Yours seem to be doing that well during the day but night is when you have your problems.
At night my adults sleep on the roosts. The adults do not let them on the roosts. The chicks sleep somewhere else. That might be on the coop floor or on something other than the main roosts. To help keep them out of my nests I put up a juvenile roost, separated from the adult roosts, a little lower than the main roosts, and higher than the nests. Your coop might not be big enough to do something like that and get enough separation between roosts. You may be OK with them sleeping in a nest as long as the others aren't laying eggs in there.
There can always be exceptions, sometimes mine mingle more than other times, but typically they maintain this separation until the pullets start laying. Then they are accepted into the adult pecking order.
To me this sounds like it should work.
That coop does not meet the generally suggested minimums you see on this forum for your 9 chickens but since you have a secure run it should work once they are fully integrated if you leave the pop door open all of the time so they can get out when they wake up. I don't know where you are located though, your winter weather may prevent them being able to get outside when the sun comes up.