First, I personally like your plan for handling bedtime. I totally agree that this is Cooper's attempt to control the pack's den. You, however, are the pack leader and it is your den and if you say no squabbles over bedtime, then that's how it should be. Cooper and Lady can work out their doggie issues at other times/other places...but the bedroom is for sleeping, not starting trouble, IMO.
In my house, if you can't behave at night, then you're not welcome to sleep in our bed/bedroom. I know Ollie's our dominant one, but he doesn't get to growl at the others from atop our bed. He's learned that if he growls, he's off. Obviously, I don't invite trouble by then allowing the others on the bed instead, but one night of sleeping on the floor once in a blue moon is enough to reinforce that the humans in his household make those decisions, not him.
I don't see the crate as "punishment" for Cooper and the bed as a "reward" for Lady -- that's humanizing the situation -- what you're doing by leashing/crating is controlling who goes where and that's what the pack leader (you!) does....same as what Cooper was attempting to do. You making that decision is totally within your rights as pack leader. You could swap who's in the crate every few nights, as well, just to be clear who's making that choice.
Doorways are often places of conflict. Lilly's breeder has two girls -- one is Lilly's grandma, the other is an adult b###h -- and if grandma goes out first, then the younger b###h gets snarked on. If grandma is the last out, then not a problem. Honestly, it's easier on everyone for the human to play gatekeeper and avoid a scuffle rather than just let them work it out, especially since a b###h fight in a tight space can be b-a-d. That's the only situation that was problematic for those two and it was fairly easily resolved by a bit of intervention.
That said, I wouldn't interfere in other dog discussions that don't involve my rights as pack leader. They want to go the yard and yell about a rawhide? Fine. Want to grumble over dog #2 being in dog #1's bed in the living room? Okay by me. The difference here, I think, is the whole concept of the den and who controls it.
Pack order is fluid as Sara's said, but it generally doesn't flip-flop overnight. One thing to watch for is if Lady is feeling okay. Even changes in blood chemistry (thyroid levels or anal gland issues, for example) can cause a dog to smell differently and thus make the rest of the pack react. They also pick up on subtle clues about declining health, so if this has been sudden and Cooper is generally not a pushy type of boy, you may want to see if Lady is doing well.
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