So Erdogan asks Musk where his wife is. This is a neg. Erdogan sells himself as a traditional Muslim politician, and he lives up to traditional Muslim family values—Musk, however, does not. So Erdogan makes an issue out of it to establish dominance—if you don’t have rockets, you can have superior traditional values, anyway…
Why does Musk bring his child? Obviously, he doesn’t have to—he must have support staff as well. I don’t think it’s a gambit to unsettle Erdogan, I don’t think Musk needs something from Erdogan. I think it’s two things: first, Musk is a Cancer and Cancers genuinely want to protect and care for their children—place a lot of emphasis on their kids; second, arrogance—Musk doesn’t think normal social rules apply to him, especially with an unimportant man like Erdogan.
So Erdogan’s neg is a legitimate response to disrespect from Musk—and an attempt to make up for the fact he has been disrespected. However, note that when Musk spoke to Netanyahu later that day (I believe on the same day, but close to the date of this meeting anyway) the child was not in evidence—because Netanyahu is a “serious man” whom Musk has to respect, and would be punished if he failed to respect.
It shows us something about the power differentials between Turkey and Israel, and about the men Musk has to be afraid of and/or needs stuff from. It also shows Musk isn’t a classy man, not a gentleman, because a classy man would treat Erdogan with respect even if he was his inferior or he disagreed with him—but to Musk he’s beneath contempt.