Ok...
The way you have worded your post has prompted a very strong reaction... if people have taken the right meaning from your post, they have said everything that needs to be said on the subject, so I'm just going to proceed on the assumption that you are considering rehoming your dog via a reputable rescue...
I am currently on maternity leave having had our daughter 6 weeks ago. And I can honestly say that my priority from knowing I was pregnant has been to ensure I was able to care for our new addition as well as our existing responsibilities. Honey didn't ask us to start a family - we made the decision initially to have a dog and later to start a family, and I think we owe it to her to ensure that she is included as just as important a part of our family unit as she ever was.
You say you will both be working full time after your wife finishes maternity leave - surely this was the case beforehand? So what arrangements were made for your dog then? Can you not look at day care for your dog, or a dog walker?
How does your wife feel about this? Has she previously been committed to the dog, but is just struggling now, or has the dog always been "your" baby and now she feels her time is being stretched in too many directions?
The general tone of your post sounds like you haven't considered the impact starting a family would have on your dog, or his place in the family. That you have focussed all your energy on your new baby and left your dog's needs out in the cold. If you can't put in the time to meet the needs of your dog AND your baby, then, yes you are better off rehoming him
through a reputable rescue. However forgive me that I don't have a lot of sympathy for your plight - I was running around doing an agility lesson for Honey 8 days before Isobel was born, and we are back to the agility lessons tomorrow, it has been a priority to me in these early weeks that Honey has had the same level of exercise she is used to (a good long walk every morning and a shorter one most afternoons) and I have mastered the art of clicker training while breastfeeding. I have dragged my husband along to Honey's socialisation group, so that he could focus on the baby while I focussed on the dog (but I was available to feed if needbe). And I used my first opportunity to go out without Isobel (courtesy of a bottle of expressed milk now she's reached 5-6 weeks) to take the dog for a long walk with lots of training included. Yes, life has changed for Honey, and she's a little put out by some aspects of it, but we've made sure we've put in the effort to make those changes manageable for her.
To be blunt, yes you should have considered this before you bought your dog - but if you can honestly see that you are not meeting his needs, and will not be able to in the foreseeable future, then please do rehome your dog via a rescue to a home who will give him everything he needs - you owe him at least that much..
Editted to add - as Jane says, if it's at all appropriate, your first port of call should be your dog's breeder...