My answers are in CAPITAL letters. I'm not shouting, just trying to make it easier for you to see:
Well, that's being generous. (why did he say that) TO SAY THAT WHEN ELLEN SAYS HIS TWINS HAVE MOVED OUT SHE IS BEING TOO KIND TO THE TWINS, BECAUSE IT IS NOT REALLY TRUE. THEY HAVE NOT MOVED OUT COMPLETELY.
They're never going to move out unless you [make] them, right? (is it nature to use make here, is it identical to force??) YES IT'S VERY NATURAL. AND YES 'MAKE' HERE MEANS 'FORCE'
And then after that wrap, my wife and I.. (what's wrap here)'WRAP' IN THIS CONTEXT MEANS 'FINISH FILMING OR RECORDING' - SOMETIMES WE USE IT IN EVERYDAY SPEECH TO MEAN 'IT IS FINISHED' WHEN BOTH THE SPEAKER AND LISTENER KNOW THAT IT IS BEING USED IN A SLIGHTLY JOKING MANNER
But this time we took the whole gang. (is it normal to use "whole gang"?) YES. IT'S SLANG, BUT IT'S APPROPRIATE FOR THIS TYPE OF RELAXED CONVERSATION
It writes itself. (totally no idea) HE HAS JUST EXPLAINED THAT WIFE HAD SAID SOMETHING FUNNY (IN HIS PREVIOUS COMMENTS) - SO HE DOESN'T NEED TO DO ANY WORK WRITING A TRADITIONAL JOKE - HE CAN JUST TELL THIS STORY AND MAKE PEOPLE LAUGH