I was able to use the mover's coupon + $50 trade-in coupon at my Best Buy here in Phoenix, but when my mom tried to do this at a Chicago-area Best Buy store, they absolutely refused to take the mover's coupon.
My mom traded in her first-gen iPad mini (16GB Wi-Fi) and received a $150 gift card and $50 coupon towards an iPad Air 2. When she presented the 10% mover's coupon, the manager spent 30 minutes examining the fine print on both coupons and finally decided that, because the $50 trade-in coupon states "Not valid with any other offers," she could not use the mover's coupon. She even gave the manager a copy of my receipt from the Phoenix store showing that they took both the $50 coupon and the mover's coupon, but the guy would not budge. She ended up just forgoing the additional 10% from the mover's coupon and using only the $150 gift card + $50 coupon.
I'm thinking of reaching out to Best Buy's corporate office to see what they have to say about these inconsistencies.