It was a bit ridiculous for Kiritani to complain about Azumane taking care of a child that isn't his, when she's cheating on her husband...presumably 👀; ever since the chapter where he had his full beard(chp 8), I'm somewhat starting to doubt she is still married like she claims she is. No proof, just a gut feeling based on her reactions, and the fact that it feels like she's at her current position because "Azumane is still there". It'll probably be a while, but if that's the case, I can't wait to see what her full story is.
As far as the teacher goes, she seems like a nice woman. Nice for the barkeep to kinda set them up, but I do hope things stay platonic for now.