We had a similar situation. We have two mutts, who we love dearly. After moving to a rural house with land, we thought our dogs would be loving life. Well, the in-ground fence was completely useless, since the pain of shock was worth pursuing whatever they were chasing. They ended up on cables, tied to trees in our yard. Then, we had a surprise baby and I could not handle the amount of dog hair on the floor when the baby was crawling. Stuck to her little fingers like glue. Ick. They started sleeping in the garage, on beds,with a heat lamp when it was cold. They were neglected(by attention standards, only), in all honesty, for months. That was NOT the life we had intended for them. We decided that we needed to do something and had them trained. It was money well worth it!! Now, they are the most well-behaved dogs! They stay on their beds while in the house and except for an occasional lapse, they stay with us when we are outside.(dang rabbits, LOL!)
Ok, so the trainer said they needed to be exercised every day. I stressed about that quite a bit, since winter was coming up, and how do you exercise a dog in 5 feet of snow, with a toddler?? The trainer said that even mental exercise counts. So, just giving the dogs a few commands and having them have to "think" about what they are doing will count as mental exercise. It takes way more ambition than I have to get them outside for an hour of exercise every day. It just cannot happen with our lives. But, anytime we go outside, the dogs come with us. I throw the ball for the one who LOVES to fetch. Given that yours is a golden, he will probably fetch? Throw the ball for him, while your son plays outside. Even when the baby comes, he/she can be in the stroller while you play fetch for a while.
Also, since they are trained, we go for walks and they stay right with me. I can run, walk or rollerblade and it's great exercise for them. My kids have no problems handling them, because there's nothing to handle! They know their commands and will come, sit or go to their "place" (bed) when told to.
I know how hard it is to give dogs the attention they need. Believe me. If you know of someone who would give your dog a great home, then maybe it would be the right decision for now. I understand that. But, maybe it would be worth your while to look into training. It's not just about heeling or not jumping up on people. It's a real mental breakthrough. I don't want to say it makes them more lovable...but, it makes them easier to handle, therefore, less frustrating and less work. Instead of being super hyper all the time, my former hyper dog is way more calm and seems to be proud of himself for being so well behaved. Sounds silly,I know. We have had many people be astonished at the turnaround. I wish you the best of luck!!