WHen they vote for Trudy, if she can stay, they say Bray and Trudy can't vote because they are not apart of the Mallrats. But Bray had already been accepted in. And after Trudy gives birth she's says to Lex "Bray invited me to stay" and Lex replies "and who's he to do that, some of us didn't him here either" (basically acknowledging he is apart of the Mallrats even though he doesn't like it.)
Firstly, I don't think they were officially the 'Mall Rats' by this point, they were just a pretty much un-named 'tribe' staying in the Mall. I'm on episode 12 right now and they still haven't picked a name.
Secondly, Bray wasn't voted in. Lex points out on numerous occasions, like the one you mentioned, that neither Trudy or Bray should be accepted because it wasn't voted in that they could stay.
I don't really see the plot hole. Bray was never voted or accepted in, and Lex acknowledges that?!
18 seems a little young to be mayor. What were you, like, 12?