You could ask to see her for 15 minutes between family commitments and have an espresso. From what I understand she insinuated that she would like more and that going to the movies is not her thing. She is interested. It's not the time to play hard to get, I think the best move is to see her as soon as possible and not fade. Tell her you have to see her for 15 minutes and figure out something that feels important to a woman to tell her during these 15 minutes. If you're lucky, she will call you after the family commitments and ask to see you at night.

When you see her for a few minutes, tell her something personal about you that is related to her. Something like "i was looking in the mirror and I thought I heard your voice calling out for me from the other room, telling me to ......." or something like that, or how you think about her, a scenario in which you would see her, inspired by her way of being. Something like "when I think about you, I see you dressed in a beautiful blue dress, praying in a dark chapel that your lord will come safely from battle" or something that you see her doing. It will make her day and she will not be able to stop thinking about you while on family commitments.