It seems like all my small/temporary/quarantine coops resembly enclosed rabbit hutches. So, how about one of those? I don't know how much they cost, but as a short term solution you could get one of those and close up the sides. They don't need much, even in the cold, when they are healthy. I can't tell you how many times I've provided shelter and given the choice they'll roost on the top of it. Given that you can provide a pen you could get away with not providing the standard 4 sqft per bird for a short period of time. If you did it this way, when you do build your coop, you'll still have this to house recovering, or new birds during quarantine. Which it sounds like you'll need in the future..
The set-up I use for temporary housing like this is a 10x10 dog run/kennel with a small wooden rabbit like hutch. I also put a tarp along the outside of the pen to block the prevailing wind. As long as they have protection from the wind/draft they're usually pretty happy. As I said, more often than not some of the chickens will sleep on top of the hutch instead of in it since they have the wind break. I can provide a pic if needed.
Good luck. Hope you can help out those birds. I have a daughter the age of your daughters and she's very involved with the chickens and loves going out and visiting/playing with them.