Try to stop stressing about testing neg. You DON'T need a US based MD for the recovery letter. Hundreds of US citizens have used recovery letters from local MD's to fly from Thailand (where I travel frequently) and also from various countries in Europe. In fact in Thailand (just b/c I know more about it) there are telehealth clinics that will assess the positive test, verify no symptoms and produce the required letter.
If you just go to a local MD/hospital/clinic when the requisite time has passed with positive test result (or maybe a Irish telehealth service) they can issue the letter of recovery. If you can relax and stop worrying your daughter might be able to enjoy her last few days there (and you too).