In the bar scene near the end, she discouraged Somiya from getting remarried, gave him a big kiss, invited herself over to his place, and gave him a "look" while flashing her tongue.
Or am I reading too much into this?
Yes, you are.
"I'm a leaf on the wind, watch how I soar."
Rise of the Lycans: 8/10
Friday the 13th: 5/10
It's an important moment in the film, so you're not reading too much into it. Aya's behavior IS provocative, given the time and culture of the film. And we've already seen how 'modern' and 'liberated' she is, so I think even Japanese audiences can't help but wonder what her intentions are. Even Shukichi practically pleads, 'Really, come and visit me.' It's all something to ponder.
The scene parallels the earlier one with Noriko and Onodera at the same restaurant, so analyze away what that might mean.
But after all, I think she's just having fun flirting. That kiss on the forehead is all he's getting.
It definitely looked to me like the two might get together someday. She was flirty and he was open to it.
"Will you really visit me?"
you are mad, do you think you are watching a japanese filthy porn featuring old man and his daughter-in-law after his son has been dead?
you are filth and disgrace.
And yet Ozu's later film An Autumn Afternoon briefly examines an older man who remarries; to a much younger woman.
"Bars during the day are like women without make-up"