Need help with my chicks

I have 4 chicks born 1/2nd June to Hen outside and 2 chicks born 6/7thJune from incubator Lost the mum, all other chicks died in shells and these had to be hand hatched!
Today we had all chicks together for about 2 hrs on lawn with Hen. A week ago she rejected one now they all played together with no fighting and she was fine.
We want to gradually intagrate. We cannot leave them to get on with it - as the outside chicks are bigger and know when they get cold to go under mum the little ones just sit and get cold so we have to put them back in the brood box. So we can;t leave them yet. - Anyone know if it would be possible for us to get mum hen to take them and when we can try to leave them over night. It is raining and cold here a lot of the time. But warm sun today!!!!!!!! How old before the chicks can go outside perminantly and how do I sex them????????????

 

Thanks everyone - I knew about the putting the baby chicks under mum at night kind of thing. But our chicks are kind of way past that stage so its kind of not a newbee kind of thing. I mean Bertha has been off the nest for agess! She practically threw her 4 out in the cold after like 2 days and never went back to the nest! I did think gosh wont they get cold and die thinking of the temperature in the brood box? But no - they are fine and growing like mad. But our others seem to miss out on loads of stuff. In a box they don;t get all the being a chicken lessons we see mumma hen teaching the others. It is kinda funny to watch them all in a line and mumma bird teaching them digging and pecking and stuff. Then I look at the wee orphans and they don;t get that. We were thinnking today went well in that they all were together for a long time without any issues exceot when all the others go under mum our 2 sit there like twits getting cold as they don;t know what to do!!!!!!! Never having had a feathered mummy before!
So I am in a bit of a dilema really. We were thinking of just doing well supervised daily visit if its warm. Then as they grow increase the time. Once Bertha starts to lay again I figured we would split the big coop run into two and biuld another coop for the wee ones down one end and put Bertha back with the grown ups. They can all still see each other and it will kind of be a natural progression for the younger birds. I mean they all have to live with each other in the end? I figured when the time is right we would just take the partician away in the coop and they would all be in the big one then. - I think we have 2 roosters - they will be found good homes else where/ or if I am really unlucky the 4 I think are girlies and am fond of will end up the boys???? Wish I knew what I was looking for?????? Anyhow what do you all think of the plan feedback would be good to hear???? We are not leaving the chicks out at night at all with the big hen just in case she pushes then aside at night when its cold and we can;t be there to rescue them. - We will only do it when it is just all the chicks together !!!!!!!!!!!! When there a bit older? SOme of you sugested different times I will see how they grow, Just glad the 2 tiny ones survived as they were very very weak and we thought they would die. Thanks much!