Dear Cubicle Coach: My boss just offered me a promotion, which means working with a supervisor who doesn't like or respect me. Should I mention the problems with the little boss to the big boss?
Dear Moving On Up: No. Part of moving up in the ranks is the expectation that you can work things out for yourself. It's likely the immediate supervisor signed off on the promotion, signifying her willingness to move on, so get to work mending fences. Ask her out for lunch and, if you share my facility with bullshit, even offer, "I'm looking forward to us working together, and I know your support for me was one of the main reasons I got this job." Let her think you owe her a little bit; get her invested in your success. Then start working your ass off on that new gig.