I read a story quite awhile ago on Archive of Our Own but for the life of me I cannot remember the name of it. It was where John was staying with his brother and his family because he was severely injured on a mission and was sent home from Atlantis. Rodney ends up showing up on their doorstep and finds John sitting outside by the pool. John's sister in law offers him lemonade and Rodney calls the mountain to have John's medical records released so that he can see a doctor about maybe getting his leg fixed. Rodney ends up using a friends apartment that is close to a hospital so John can get treatment.
I know it's not much but right now it's all I can remember.
Thanks for your help!