I've read most of the replies, so excuse me if I'm repeating anyone.
We have a milder version of this at our house.
One problem is that DH works 2nd shift with very rare days off and I am the one that does 90% of the hands-on parenting. We've always had problems with being on board together with the same approach. DH feels that, on the days he has off, he isn't a part of the family any more, he isn't around the kids that much, we have a routine set or rules in place. We've always had problems, even before, of our oldest asking me for something and I'll say no and so he'll go ask Dad and Dad will say yes, and we'll end up in a huff over what is okay and what isn't or what plans I had for the day or what had happened during the week that Dad didn't know about. Another thing he'll do is make "threats" but he isn't home to follow thru on them, and they're things I have no intention of enforcing.
By the way, my kids lost their doors a long time ago. We have a door on the bathroom and our bedroom, and that's it. Oldest DS has a sheer curtain in the doorway, which he flings closed when he's mad, which is kinda funny. But the doors have been gone for so long that they don't think anything about it.
We just started a new "behavior plan" at our house about 3 weeks ago. Their game-time is directly correlated to their behavior. As part of the initial family meeting, I made 4 lists... Things parents have to do (shelter, basic utilities, basic clothing, nutritious food, medical care, that sort of thing), things parents don't have to do (provide computers and video games and toys, junky food, chauffer 6 blocks to school, let friends come over, vacations, etc etc)... things kids have to do (be respectful, try their best at school), things kids don't have to do (get a real job, pay the utility bills). This was a real eye-opener for my boys. I told them they were more than welcome to take the lists to school and show them to the counselor or whoever, if they didn't believe me. It also made it perfectly clear to everyone at the meeting (cough cough) what was required. That was our stepping-off point. I had simplified it because my kids are younger than yours, but the idea is the same. It might be an interesting experiment, if your kids are cooperative, to make some lists like that and ask them what they think goes in all the categories.