I read your post to my family. No one can believe that your husband isn't supporting you 100% in this and that he hasn't seen that this other person isn't a friend at all.
My DH suggested that the next time he comes over with the dog, have one of your friends, who lives close, on stand-by. While you keep the little boys (sorry - DH and his friend) busy in the house, have your friend take the dog on a car ride a looooong ways away. (The further away the better.)
You can then say you don't know what happened to the dog when the pretend friend goes out and can't find his dog. Since you were in the house with them - they can't say you did something to the dog.
Now - none of this is fair to the dog... it isn't his fault his owner is a blooming idiot.
I had a dog that was born with only two functioning brain cells
but she was my favorite little sweetie. I just had to take care to keep an eye on her all the time as she had no sense whatsoever. She has died. I still miss her terribly; she loved everybody but thought I was the cat's meow in her life.
Good luck with whatever you decide. I hope your DH grows a backbone and realizes where his loyalties should lie.
I'm editing this because I was doing several things at the same time last night and realized that I didn't finish our thought and it sounds bad as it is. We didn't mean to have the dog just dropped off somewhere it should be taken to a shelter. Then, you can suggest that your DH's 'friend' look at all the shelters in the area and he will find his dog. He will not only spend his time looking but will then have to pay to get his dog out. Maybe (I stress the maybe since he doesn't seem to be too bright) he will leave his dog at home in the future so as not to take the chance of losing his dog at your place again.
We would never advocate to abandon any animal. We aren't even big on taking animals to shelters but there are times when that is the best solution. Sorry I screwed up our response by not paying better attention to what I was typing.