Great post mate; it's so annoying, even yesterday night when I went to babysit my cousins kids and my grandmother was coming over as she hasn't seen them or her daughter (their aunt) in awhile and wanted to talk.
First thing that happens, the boy of theirs run over in underwear, says hi, then goes back to playing kingdom hearts. A few seconds later his younger sister peaks around the corner and say hi to me, and then before she can even finish saying hi my grandmother starts squeeching an couple inches from her face "HELLO (X), AREN'T YOU GLAD YOUR (me) IS HERE" and just weird things.
She continues doing that for about twenty seconds at least moving closer and closer to her face, with her (the little girl) just staring awkwardly and nervous-looking, panning over to me once or twice.

No no no no NO, spooky grandmother, stop talking to her like she's a literal infant and that she has no personal space or feelings of her own. She does, and she's four, you definitely definitely DEFINITELY shouldn't be baby-talking her unless she asks you to.
She was just coming by to say hi to me, and to you, and then probably give me a big hug like she usually does. She didn't want to be spooked and borderline threatened by you. And once you spookedo ff, she did exactly that, showed me her dress, asked me if I liked it, and then dragged me around places and showed me her new cool pillow that changes color depending on which way you rub it.

Don't demand a greeting or try to touch him, hug him, or grab him from his parent's arms.

This is what my grandmother always does. Babies (and toddlers) always cry and flip their passies because not only is she spooky, but this is downright inappropriate in my opinion.
Worst thing is she's eighty-something, wobbly as all get-out and really does not hold babies correctly at all.
She always talks about babies/kids as if they're objects too of course, that's how these people seem to always be, and that ticks me off.

Anyhow;

Now I'm just ranting; but yes, so much yes in this post.
When I meet a new child, or I am not greeted happily by them, say they're frustrated or something, I'll do my own thing or sit nearby and wait for them to interact with me, or wait for a kid I know to introduce me/pull me into some game with them.
Most people really just have no fucking clue when it comes to children :/