Areteus,
Sounds like you guys already know about that trick. I didn't know it was called alpha-rolling, that's cool to know.
Yes, some dogs don't like it at all, but that's an important clue to how the dog sees itself in the hierarchy of life. The dog really does think it's boss, and doesn't want to be put in a submissive position. My take is that on that kind of behavior is that it is more important than ever to straighten out who is in charge. The dog is telling you loudly and clearly that it thinks it is dominant over you.
I believe that animals understand us when we talk to them. I remembered last night after posting here that I used to talk to my dogs while I had them down. I would explain, in a calm tone of voice, something like, "You're awesome, Bud, and I love you very much, but you do NOT give orders around here, you are NOT in charge, I am, you do NOT bite around the food dish, you do NOT growl," etc. Everywhere there are caps I would not only raise my voice a little bit, but give the dog a firm little shake with the hand that was on its throat. I was always strong enough to control my dogs, even if they wriggled and squirmed a little bit.
I know, I know, I'm making it sound like it always works, and it doesn't, but I think it's worth a try. If a dog wouldn't let me control it like that, and tried to bite, I would call in a professional trainer.
We have a kitty now was on his own outside for a long time. He is learning how to live with people and another cat. Sometimes it's a struggle. But once you take on the animal, you're in forever.
EDIT: As far as alpha-rolling being abusive to the dog, I don't see it that way, but I never crossed the line. I am a hugger and a kisser with my animals, but I try not to let them think that they are dominant over me. I feel that not training a dog well, especially if that dog interacts with other people, is doing a disservice to the animal. (If I live on my own with the dog, and nobody else ever sees it, the dog's behavior is only my business and the dog's.) If I am squeamish about showing a dog who is in charge, I may be condemning that animal to a substandard life. In extreme cases, a growling or biting animal may be disliked by most or all people that it runs into, or even risk punishment or death, if it bites somebody in the street and has to be put down. A misbehaving animal is not any more cute than a kid swearing at the table or throwing food at guests. I would rather show off a well-trained dog than make apologies for an animal that is bothering people. Granted, like people, some dogs have extremely difficult personalities to deal with, and there isn't much any of us can do. It also goes by breeds. I used to have a dog book that listed degree of dominance over owner as a characteristic of breeds, along with hair color, appearance, etc. Some breeds of dogs have a tendency to exhibit a lot of dominance over their owners, and it is often subtle. Anyway, even if we are uncomfortable in struggling for dominance with dogs, the dogs certainly aren't uncomfortable struggling for dominance with us, they just do it, it's a part of life to them, and some dogs are willing to take charge unless we lay down a few basic ground rules. So it's best to recognize that a struggle for dominance is going on, we can't wish it away, and we need to do our best by the animal by letting it know that it is not dominant in the house. The animal will not be cowed or shy or sad after that, and everyone, the animal, the owner, and the owner's guests, will get along better.