I get being dense when it comes to romance. I really do get it because apparently I'm the same way, but the Duke is kind of making it obvious he wants to spend time with her. She should also be aware, since she cares about kids so much, that the best way to raise a healthy and mentally stable child is to have BOTH parents there for them.
It is only natural to make attempts to get the Duke and Ain's relationship to be better even if she herself wishes for no romance with him. It confuses me as to why the thought hasn't even occurred to her and I'm starting to wonder if it is a cultural issue that I'm not aware of.