Dog won't stop

A year ago I wanted a dog, I asked my fiance what he thought of it, he didn't really want one at the time, but we ended up getting one anyway, one that he said he always wanted. It's a Norwegian Elkhound, I didn't know anything about the breed at the time, I just figured he always wanted one, and I want a dog so let's get one.

Well I regret getting this breed so much, our dog barks constantly, it's insane how much he barks.

We just moved into our new house, and while we were getting things settled away, my aunt was watching our dog for a few weeks, she and her husband are very well experienced with dogs, and they love them all. But she had a lot of issues with our dog, because of the constant barking.

I can't put him outside without him barking the entire time, like he runs to the fence and just barks as loudly as possible until I literally drag him back into the house

Nobody can approach any door without him barking

No doors inside the house can be opened or closed without him barking, including bathroom doors

He's after barking even when I close the dishwasher

When I get down and clean the floor

When I was cleaning the table today he was going crazy

I lost it when I picked up a paint can in our nursery, (I'm expecting a baby soon), and he lost his mind barking.

It's all day long barking, no amount of training will get him to stop. He knows he's not allowed to do it, but it's like he can't stop himself.

My daughter has days where she can't handle his barking and locks herself in her room to get away, but she also loves our dog, even though he doesn't like to play with her either

We took him to a doggy day care for the weekend one time, and we had to come back early because they couldn't handle him

We talked to a trainer and he said there's not much that can be done, because he knows the difference, he just doesn't care

I'm at a point now where I can't handle it any more, and I'm looking into rehoming him, I discussed it with my fiance and he of course is sad, he doesn't want to get rid of him, and he likes the barking, because he let's us know when anyone is nearby, but I have no peace, and I don't want our new neighbors to hate us, and I don't want the dog to wake the baby all the time.

In this situation would you keep the dog, because your fiance wants him, and the commitment, or rehome him because neither the dog or yourself is happy in this situation?

We did try a collar, that beeped, vibrated, then shocked if he kept up barking, then got more intense the longer he barked. He actually barked so much the collar must have short curcuited because it actually burned the fur on his neck off. So we ditched all collars after that