How long has Cooper been with you? At first is the "honeymoon" period, where he was content to be submissive, while he figured out the dynamics of the family unit. Now, in his own posturing way, he is challenging her. Since she has always been in the bed with you, keep that the same. For the time being, Cooper should sleep in a crate. You have to determine who is the alpha between them. Since Meggie has always come first, Cooper needs to learn that will not change. You can't have two bosses. Eventually, he will learn his place. Time is wonderful for solving these issues.
We've been going through this in our house some what. We've had Toby for 4 months now. I'd been treating Sadie as the alpha dog, since she's been with me the longest. However Ginny was constantly competing with her and when I through Toby in the mix the grumbling and lip lifting started to become more frequent.
When I started treating Ginny as the alpha instead, the balance shifted and everyone seems happy now, the grumbling and disagreements are completely gone.
If Meggie is trying the hardest to be alpha, then let her be. Missjennygirl's suggestions were spot on (IMO), I just want to add that Meggie, as the alpha, should get everything first, including feeding.
Ginny always wanted to check out everyone's bowls, which was part of my problem. I new feed her first, away from everyone, which has been a huge success.
If Meggie is used to sleeping on the bed then have Cooper sleep in his crate or in a dog bed on the floor. This is the only thing in our house that hasn't changed. Sadie sleeps on our bed with us and Ginny in her bed, even though she's the alpha. This works for us because Ginny happens to LOVE her bed and she tends to wake us up when we do allow her to sleep with us.
I know it sounds bad when they disagree but try not to worry yourself, it IS something you can fix.
danisgoat has a really good point too, it can't hurt to have her thyroid levels tested.