2. Since Mary has just moved to town, I will bring her with me to the luncheon on Sunday.

If I'm talking to Angela and we're both going to be at the luncheon on Sunday, why not say "I'll bring Mary with me"?
Seems kosher enough, Bingley. Remember the deixis rule the other link talked about?
With or without Angela, your being at the luncheon satisfies the rule; bring, entailing movement towards you.
If, however, both of you are going to the same luncheon, then the rule is doubly satisfied, it could be, bring 'towards' you or bring 'towards' Angela.