This was a total treat. Eileen Prince = Irma Pince FTW!
I adore this kind of Minerva/Severus--unsentimental but caring, with just the right amount of snark and competition. I also love the way Snape evolves from unsure young man to confident lover, both emotionally, and (as you hint) sexually. And Minerva's touch of insecurity at the beginning is just right.
The tension in the relationship between Severus and Irma is just spot-on, and it's easy to see how a mother like Eileen might have influenced Severus to become the sort of man he is, good and bad. The conversation between them in the beginning is wonderful, as he flits between boyishness (Snapian boyishness, anyway) and manhood.
I also love that you didn't make Filch the caricature bumbling, angry, inarticulate git that he's so often portrayed as. He's very believable here and heart-meltingly human, though not perfect.
There is so much that I love here, but I'm going to quote my very favorite bit:
"Maybe so," said Severus, looking down at her, "but at least I spend my time consorting with the best Hogwarts can offer, while doing a reasonably good impersonation of the same.