This is sort of an abstract way to look at things, but....you know how when you're super interested in something, you tend to be really good at it and really like it. Like in school, I was interested in music, English, animal behavior etc....so I excelled there, but I was TERRIBLE in math, wasn't interested in it. Later, when I went into the medical field, I was good in school because it interested me a lot and more education in canine behavior. Other subjects which didn't particularily interest me, I didn't do all that great in.
What if you decide to take an avid interest in the dog, as an individual and as a specie on an intellectual level, learn all you can, read books on training, their early beginnings, nutrition, genetics etc, you'll have an easier time training your pup to be mannerly and plus, you'll be looking at the pup from the standpoint, not only from an emotional level, but as a hobby, an interest, a learning thing...a study. I know this sounds sort of around the bend, maybe even sort of cold... but my thoughts are that if you dive deeply into the puppy, your intellect will over power your emotional thinking or balance with it...(not that your whole thinking is running off of emotions.) And then the rest will fall into place. Once the pup is "civilized" at around a year or two, you will have developed a real bond there and you'll be glad you kept him. They are extreme social creatures, forming very strong bonds, just like we do.
If you don't think things are bound to change though, I agree with those who said that it's better to give him up now while he's a pup than to wait.
I'm sorry you're having these feelings. It may indeed be a by-product of your post partum depression. If you feel strongly about keeping the pup for your kids' sake, perhaps talking to a professional might help sort through this too.