It helps me to remember that these things work both ways. She had just as much opportunity to greet you as you did to greet her. Neither of you are bad people. Neither of you were there for each other. It's not a bad thing to just be there for your family.
And I'll second that she most likely isn't thinking about this. My neurotic ass might be tempted to DM her, but only if I couldn't find a way to make peace with myself. I hope you find a way to cut yourself some slack ;)
That sounds like a good plan! Good luck with it :)