You're getting a lot of good advice here and aren't some of these photos great? I keep my brooder out in the coop, but we all have different set-ups and conditions. Whatever works for you.
I'll mention that daytime temperatures can be different from nighttime temperatures so in and out like you are doing sounds like a good plan. And the conditions outside here right now reminds me, pay attention to wind when they are outside. Being hit by the wind is not good for them and whatever you have them in maybe could be blown over. And, of course, you don't want them to get wet.
Just because some people can put their chicks outside at 6 weeks does not mean we all can. It depends on how cold it gets where you are, especially at night, and how they are housed. Mine were fine at 4 weeks, but it was June, there were a lot of them so they could keep warm huddling, and they were locked in a predator proof, draft proof coop. I did not let them out to the run until 8 weeks.
They are a lot tougher than many of us think.
Good Luck!!! I think you are doing fine.