I'm definitely leaning towards it just being Himawari/The Shapeshifter.
I'm not entirely sure why Ayane's mother would be near Sensei's house, so it seems a little random for her to be there, especially in a Niki Event that seems more about Ami, Sekai, and Sensei in particular.
It seems like Himawari, and those like her, still need to eat, and probably aren't as supernatural as they seem. Himawari in particular has been shown wanting a cafeteria:
Her having a briefcase wouldn't be all that surprising. She seems to need to move around a lot for her job, and she's someone that Sensei isn't supposed to remember, yet he tends to usually find her familiar nevertheless.
Not to mention that if Himawari is his and Ayane's kid from some alternate or future timeline, that he's not supposed to know about, then she's not exactly easy to get rid of. The red ink could also be a hint at blood relation.