Oh, sweet Martha,
Although pneumonia is a danger for the very elderly, it's being treated, so all that can be done is being done. Pneumonia has different causes, so maybe this germ isn't one that the vaccine targeted or maybe she'll have a lighter case because of the vaccine.
IF you'd stayed in NYC, your mother could have fallen down the steps in her building; she could have wandered away in the hours between when you left for work and the aide arrived - or burned the place down in that free time. There are endless possibile sad, bad, scary, and dangerous things that could have happened even with you there. A few did happen!!

We do know your Mom has been safe, happy, warm, well fed, and well liked where she is and while you were where you are now.
NO GUILT!!!! You did the right and only thing in moving to IN. Prayers for your mother starting. Wine tonight as another grateful celebration for her long life and sweet spirit!
(((((((((hugs))))))))) Barbara