This is exactly the kind of thing my uBPD mom would do! I get a lot out of these boards because when my mom does stuff like this I sometimes think I am the only one with such a complex mother. Plus it always takes me a while to sort out what is so disturbing about her communications.
Some examples from my life that are similar to your email:
1. I spontaneously sent her flowers for mothers day once and the next year she demanded that I send her some again. And instructed me on how they were to be sent to her work so she could show off (or promote herself somehow)
2. When I got a new boyfriend after a difficult break up she (a) first said she didn't want to know anything about it because the break up had been too hard on HER and she didn't want to know until things were serious with a new man (b) then demanded to know weird random details about him.
3. Years later, when I told her I was pregnant, she demanded that I recreate a conversation she had in her own childhood upon learning about a new sibling. She was like, "Say XXX" and totally demanded I follow along. She had been playing this scene out for years as she was TOTALLY obsessed with the idea of me having a child. Even when I was going through the break ups I discussed above.
I have many more examples too. In hindsight, I have come to see why these kinds of things bother me so much.
-They reflect the level of enmeshment she imposed on me when I was a child. I was used as an extension of her and as I child had no power or ability to know any different.
-Her demands and odd behavior are ALWAYS about her needs, no matter what. She only thinks about herself in these examples, it never crosses her mind to think about how I might be feeling or what I might need. She sees me as a means to fill her needs only.
-Like your email, usually my mom's demands are also passive aggressive. Instead of just saying, "I'd like to have a closer relationship, and I'm happy about your new boyfriend," she does things like this instead.
For me, I have totally stopped giving in to demands and odd behavior like this. The nice part about email is that it usually gives me a few days to craft a good response. Now days I usually call her out on the odd behavior "This email has some strange questions, requests in it- I'm surprised you weren't more happy for me." and also I only give her minimal info.
And I would say no to her idea of coming for a visit.
Good luck,
