While it is a rare genetic defect, there is such a one and it's well worth investigating the posibility that your daughter has inherited the trait you had to deal with. Since what she has is being called "atypical" pneumonia and is being treated with multiple approaches, it seems likely this is a familial thing. It's definitely worth a look, and even if your pediatrician feels this is unlikely I personally would request referral to a genetic counselor just to be certain this is not a heritable trait, as it could then turn up in subsequent generations and knowing if it's present is always useful information. If it's just a bizarre coincidence all the better, but this should be ascertained before writing this off to just bad luck. It seems a little too close for that.
I hope this is helpful. Good luck to you and please follow up with us here as needed.
John Kenyon, EMT, CCT
Non-invasive cardiology tech, Emergency and Critical Care technician, Critical Incident Stress Mgmt. specialist