I say put it up on a shelf (or in storage) for a while to give yourselves time to cool off. And maybe comment back on that thread on Facebook with "btw mom, this is a public forum and we can all see what you're writing. ;-)"
Or maybe not. Lol.
It doesn't sound so much like drama to me (at least what I was picturing) as it does she's trying to throw a pity party for herself. Some people are just Debbie Downers like that and will take every comment anyone makes and turn it into a "look at meeeeeeee" sort of thing.
If it helps, you could see it as a sign that she's deeply emotionally insecure and is probably very miserable on the inside. Sometimes that helps me have compassion for other people's annoying behavior. Then I'm able to make decisions from a calmer place so I don't stir things up worse or stuff it under the rug (both different extremes to avoid).
I would ask her if she sent the gift. And then say thank you. And let it end there. And if she wants to continue her pity party you could say," it sounds like this adjustment of your son getting married and having his own family has been a difficult one for you to adjust to and embrace positively - maybe a counselor could help you find tools to deal with your feelings so we can have a positive relationship."
But sometimes talking "normal healthy person" language makes crazy relatives foam at the mouth.
(Which is a little entertaining at least.)