If you read through this forum, the majority of us have no real problems when we let a broody hen raise chicks with the flock. I’ve never had a problem with a broody hen failing to protect her chicks or being able to protect herself. Yes they are living animals so you will hear some occasional horror stories but those are the exception, not the rule.
We all have our own goals and set-ups. I’m not raising mine for commercial purposes, just a small flock for meat, eggs, and to play around with breeding and genetics. I’ve never had a hen go around killing chicks and seriously injuring other hens, but if I did I’d eat her. I’ve done that with hens and roosters before, remove them because of behavioral issues. But that falls within with my goals of having a peaceful flock. Others have different goals. To me, there ae too many good hens and roosters out there to put up with a bad one.
My suggestion is to try integrating this weekend like you were thinking. See what happens. I don’t offer guarantees, I know bad things can happen with living animals, but I think you will be pleasantly surprised. Most broody hens take good care of their chicks, most other hens don’t go out of their way to harm the chicks.
If you are going to have problems, in my opinion it will not be when the chicks are with the broody hen. You’ll have this same issue with your brooder-raised chicks, by the way. After the hen weans her chicks she goes back to the flock and ignores her chicks. The chicks are left on their own to make their way with the flock. The hen will have integrated them to the point the others accept them as members of the flock, but the immature chicks are still at the bottom of the pecking order. If the chicks invade the personal space of the mature hens they will possibly get pecked. It’s bad chicken etiquette for immature inferiors to invade the personal space of their betters. As long as the chicks can run away they should be fine, you probably have enough room for that. It’s possible you can have a hen that will unmercifully chase chicks to destroy them, but mine don’t.
Until the chicks mature enough to force their way into the pecking order they will probably form a separate sub-flock. They will avoid the adults as much as they can. If the hens are in the run, the chicks may be in the coop. If they are locked in the coop together, the older hens may be on the floor while the younger birds are on the roosts, things like that. It’s perfectly normal and natural. My pullets normally truly merge with the main flock about the time they start to lay. Cockerels aren’t that consistent, they can be all over the place as far as when they mature enough to force their way in.
About the only time I have any issues is in the coop after the chicks want to roost. If they go to the main roosts they are invading the personal space of hens up there and will probably get pecked. So they look for a safer place to spend the night. That can be your nests. I’m always integrating younger chickens with my flock, broody-raised and brooder-raised. This was such a common problem that I put up a juvenile roost. It’s higher than my nests but lower than the main roosts and horizontally separated a few feet from the main roosts. It gives the juveniles a safe alternative to the man roosts that are not your nests.
Your 8x8 coop should be big enough to give you some flexibility in there if you do need to make modifications. That helps, instead of having a tiny coop packed full of birds. You can help this process by having separate feeding and watering stations so the younger birds can eat and drink without challenging the adults. When they are small, safe havens are a good idea. When they bigger but still immature, having places in the coop and run where they can get out of line-of-sight from the older birds help. My nests are pretty close to the coop floor, it’s normal for my juveniles to hide under there when they are all locked in the coop. Or they will be on the roosts when the adults are on the coop floor. Don’t make places they can be trapped, give them an escape route, but walls or even perches high enough the adults can’t peck their feet can improve the quality of the space you have in your run.
I’m not going to give you any guarantees that you will or won’t have problems, with living animals and their behaviors life just doesn’t work that way. If I were in your position I would not hesitate to just turn that hen and chicks loose when you can be around to watch. With my experience with my flock and set-up, I don’t hang around and watch, I just walk away and trust my broody hens. But we are all unique with our flocks and set-ps. Even if it is totally unnecessary for the chicks it will make you feel better if you can be around to watch. You are important too.
Good luck!