As much as we may try to understand things, it can be nigh impossible until we've been there ourselves. If Sundance can get past the need to misrepresent things to Barbie, this may end up being a very important chance for you to be more in touch with what he's feeling, which can only help your relationship.
You've been talking a lot about your ego lately and I know you're feeling threatened, but I remember the things you wrote earlier about feeling like you were already her friend. It doesn't seem to me like you have too big an ego to tolerate another woman in the movie of your life, it's the lying and the lack of communication that are the problems.
I wonder, in a way, if he's handling this so poorly on purpose, consciously or unconsciously. Like if he does poly poorly enough you'll ask him not to see Barbie any more and then you'll feel like you have to stop seeing Butch to make things fair and then he'll get his mono marriage back.
Also, your comments about gifts were interesting, everybody really does treat these things differently. Maybe I should read that 5 languages or love book too.