In the heat of summer you need to make sure they are provided for. Make sure they have plenty of cool water and food. I keep fans in my hen house and they run day and night during the summer. You'll need to make sure the chicken house and run are secure and predator proof. Once a predator figures out there is chicken dinner to be had it will come back until all the chickens are gone.
If you lock them in the chicken house without access to the outdoor run you have to remember how heat builds up in those coops during the hottest time of the day. You may come home to find chickens that have died from heat stress.
What you suggest can be done. You just have to plan for it and provide for their needs when you won't be around. It is not the best situation to be in but I am sure you can work out something that keeps your chickens protectedm healthy and happy.
Can you make a run? If this is going to be every summer, you mind as well be ready for it. Make a nice size covered run and then you won't have to worry about it every summer. They'll be able to go out and go to bed by themselves. I'd hate to leave the poor chickens in the coop on hot days. They can free range when you are home during the week.
I second this suggestion. We are often away during the weekends and having a covered run works great for us. We used 1/2" hardware cloth around the lower 3' and buried it 6" and it has worked great. Very secure.