*** UPDATE***
In a chilling coincidence, yesterday - that is, a short time after I started this thread - the dog was found dead in our yard.
We had chicken for dinner, and as usual, I made up a plate of scraps and bones for the dog. My husband went out to give her the leftovers and called to me saying he can't make the dog come out of her clump of bushes (her favorite hide-out on her territory). It struck us both as extremely odd - she usually comes running when she smells bones. Long story short, the dog was found seemingly unscathed but obviously dead. It was a shock - she had seemed fine in the afternoon.
The worst part of it was that the first thing my husband did was suspect me being actively involved. Well, I guess I have to see this from his point of view: after the last chicken incident, I yelled at him, "don't drive me to despair - if you don't get rid of this dog, I'll poison her". He doesn't re-home the dog, makes it clear to me he'll do what he wants, and shortly after, she drops dead and it sure looks like poison. I realize it was a terrible thing of me to say, but we all say things when we are angry and I would never really do that. I think the very existence of this thread proves it: why waste so much time thinking how to convince my husband to re-home the dog, when I was really intending to poison her all along? Also, as I pointed out to him, it was Saturday and we were both home all day and mostly hanging out together. When exactly would I poison the dog, and wouldn't it make more sense to choose a day when he's not home?
Then, our neighbor came to help bury the dog, and he suggested it might be a snake bite. It was like a lightbulb turning on, because not long ago we caught a large and deadly snake in our coop (I posted a picture of it on another thread), and unfortunately, while we were trying to figure out whom to call to re-locate it, it escaped. We should have ignored the "endangered species" BS and whacked the snake on its head with a rock. It's highly likely it's still here somewhere, and it's perfectly capable of killing a large dog - its bite can be deadly to humans if untreated, especially in hot weather.
So, at least my husband realized I wasn't responsible for the death, but he was still bitter towards me, saying things like "you must be happy right now". Which is NOT true. First (in my rational mood), I wanted this dog to go to another, better home, not to die. Second, I wanted this decision to be made between my husband and myself and to mark a new chapter of better co-operation in the future. Circumstances decided in "my favor" this time (rather tragically), but this doesn't prevent him from planning to get another dog. He actually began talking of it about half an hour after the burial. I was horrified, of course. I asked him please, PLEASE not to do this to me and started listing all the reasons why we don't need another dog, especially right now. He gave me this dirty look and said, "if you don't get off my back NOW, I will call someone tonight and there will be a new dog here TOMORROW." Just to illustrate what I'm dealing with. If I press too hard, he is perfectly capable of doing things he doesn't even really want to do, just to prove to me he's the boss.
Again, thanks to everyone who commented. Things weren't good between me and the dog, to say the least, but this comes as a terrible shock.