I think you are getting it. Leave her wanting more (conversation, your attention, being with you, etc). But let me give you a hint about going places as a couple or as friends. Don't do it. This is her wanting to eat cake. She only wants to use you to present a deceptive persona to others. So, I'm glad you did not go with her.
As how to greet her, I think the checkout clerk anology works. You smile, speak, if she offers small talk (the weather, how you doing, etc), pretend she's the checkout clerk. B/c checkout clerks don't really care about you. They don't want to hear about what you have been doing. Don't say or do anything you wouldn't say or do if you were going through a checkout line in your local wallyworld. You just want to make the transaction and get the heck out of Dodge.
I guarantee those actions will be much more productive than anything else. And btw, when your son turns the phone camera toward her, b/c he wants you to say something to her.......just say, "Son wants me to wish you happy birthday, so happy birthday". That takes away any question that you are wanting to pursue her. If she is turning the camera on herself and she's not saying anything to you, I suggest you appear distracted by something else until the camera is back on your son.
When you are consistent in these actions, I think she'll use temp checks, to measure how attached you are. If you don't cave, then I'll think she'll pursue you. Sit back and enjoy the show. Just don't forget it is fictional. The minute you take her seriously, she'll pull away and you'll suffer again.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!
