Thanks for the ideas.
To clarify - this would be ever day forever that I would be spending time with the dog. I don't know how I can do it because I don't have and can't afford and don't want childcare. I am married but he works so our hour and a half window between him coming home and bedtime is spent with me cooking, us eating, me cleaning up and going for a family walk and then I put kid to bed. I don't want to sacrifice family time to hang out with the dog, and it doesn't include any extra time I will have to spend with the other dog to offset the increased attention to Mr. Problem. We don't have a fenced yard. Our son is two and wants to run, so isn't really up for spending our family walk in a baby carrier. Our house is small and we can't get "help" even if we wanted it.

He is not aggressive, just pushes him over? I am not sure exactly what that means in the dog world, but I am sure it has something to do with the dog thinking he is equal to the kid. I had an issue with one of my dogs and I was thinking the only option was to euthanise (the vet recommended). But, I couldn't do it. It made me physically ill. The obedience trainer had helped me work this same dog out of food aggression and fear of men (except for DH, she didn't like men, but liked him the day we brought her home at 2 years old). The trainer said I needed a behaviorist if I was determined to keep her.
This dog was very trained and competed in some minor agility (most of which she won). I am not stranger to dog obedience.
I met with a behaviorist who said he felt confident that this dog will never hurt my son if I learn how to tell her that she is a dog and he is dominant over her. So, after doing behavior training (which is not the same as obedience training) I also feel confident that my son is safe with her. It was expensive, but being that she was 6 years old I knew that finding a home would be nearly impossible. She is now confortable around him and has learned boundaries. If you can find a behaviorist that may be the best solution. Do you have any ideas for possible homes otherwise?
Let me know if you want me to post some info about basics that he taught us. I have stories that made me believe in the behavorist versus training (for most dogs obedience training is all they need).

If I were you, I would try training. Since he is treating your kid like a dog, hasn't bitten a face or worse, I think you can improve the situation in a few weeks or months through training. It sounds like your shep is like mine- dominant and bossy but smart. We are expecting soon and don't currently live with kids, but were terrified enough to try anything. We trained our dog to stop bitting and jumping on my sisters and neighbors young kids in a few months. He had never been around kids and treated them like he treated dogs- like sparring partners.
It took a while, but I found the right trainer (like Cesear Milan, dear lord) and he improved my dog's behavior in 20 minutes (I am serious- I'm still stunned). Yes, there have been other training sessions and loads of homework, but my dog was much more aggressive around kids and other dogs than you describe. We were at the point of sending our dog back to the pound for his 3rd visit... No offense to 'positve reward trainers,' but they were dumbfounded and had no solutions for my dog's aggression. Mike at Alex Brooks in Des Plaines, IL are amazing.
Action-
If you can't walk him alone, can you do 10 minutes of exercises in the house while your child is in another room? Sit, down, stay reward with a treat. Whatever. Tug of war. Sheps are smart working dogs. Give him something constructive to do and praise him often throughout the day. 10 minutes daily of concentrated attention made a huge difference for us- even though the exercises had nothing to do with kids or dogs, his overall behavior mellowed. Friends remark that they never thought a dog could improve as much as ours, so I think a little training can go a long way.
Behavior- watch and redirect. If he starts circling your kid like a shark, or you know that meal times are the trouble time, redirect the dog. Make him sit, stay, send him to the yard, whatever it takes to keep your kid safe and change the behaviors.

Training seems to be most effective when the rules are always the same and every adult in the household enforces them.

But, if it just don't work out and you have to give him up there are some great German Shep rescue groups which are better than the pound and will keep him from being adopted into another family with kids. Petfinder.com may have a list for your area.

Good luck- and no guilt whatever you decide!

what kind of home will you find for a nine year old dog? even if you went that route, you would still have to do prevention while you found something. you're in a really tough spot. you can give him to a shelter where he will either be euthanized, or kept there indefinitely because no one wants a dog that old, or you house him with you while you try to place him with someone yourself. what i see practically happening is you will have to hire that babysitter to spent taht doggy QT anyway, just to prevent anything worse from happening in the short term.

i'm curious, what did the trainers say about how long you'd have to be doing this? did they foresee this need continuing indefinitely, or did they say he woudl eventually get acclimated to the idea?

"All persons, whether living or dead, are entirely coincidental." Kurt Vonnegut

I had to do this with my Boxer a couple of years ago. She kept snapping at Li'l Bug and eventually nicked his face, and so I took her to a Boxer rescue. It felt a bit like giving a child up for adoption (I know, I'm being dramatic) as I had had her since I was 16, but I knew it was the best thing for her. She was also jumping the fence and terrorizing the neighborhood. She did everything to let us know that she wasn't happy with us anymore, and taking her to the shelter was the best solution. If you have a German Shepard shelter somewhere within driving distance, maybe that option might make you feel more comfortable? I kept in contact with the owner of the shelter, and she kept me updated on my Boxer up until the day she got adopted. People have to pay a fair amount of money to adopt the dog out, and the dogs are usually really well cared for in the meantime. This sucks, but don't make yourself feel bad over it...your life has changed, and your dog wasn't able to change with it and that's okay.

Sounds like you already know what you need to do- the dog needs a new home. It sucks, but clearly the dog's not happy in the situation and your kid is getting hurt. When I was a kid my family had to get rid of our cat because when my little brother was born she started acting out- like stopped using her litter box and would piss and shit all over the house. I guess it was to get attention? Whatever the case, my parents tried what they could to remedy the situation but nothing was working and eventually they had to let her go. Then when I was away at college my mom gave my dog away because with me out of the house he never got any attention and I didn't have the time or resources to bring him to live with me. Both times I was devastated- especially about my dog- but when it came down to it, it was better for the pets to be in a place where they could be happy and had people to pay lots more attention to them than we could.
P.S. In the case of my dog, my mom gave him to her coworker and I was able to go and visit him sometimes. That was really great. Maybe you can give your dog to someone you know- or maybe the person you find would let you see the dog every once in a while, even if you don't know them.

who's big body would shove my little one. I just kept them seperated more. Dog had free reign when kid slept, or dog was in yard whle kid is up in house, etc...
I know my dog did not do it out of aggression, just excitment. I also felt it necessary to take dog out for ball throwing. True, I had to be more vigilant and it was a pain in the ass, but they seem to be growing into each other now. Can anyone watch kid while you walk dog?

1. Find grassy hill, throw stick/ball up/down...

To be honest, I think finding a home for a 9 year old dog is slim to none and your dog would probably feel abandoned after having him that many years.

WHat a sucky situation. I vote for finding your dog a home better suited to his needs. Maybe a home with no kids or other pets so that he can get the attention he needs without having to compete for it. It'll be sad like hell to do it but safer and happier for everyone.

Granted, I don't have an average person's patience for someone/someanimal being a dick, but I think this is fairest all around provided a good home can be found. Here are some other possibilities though:

Two walks: one with baby walking, one with baby in a mai tai while you toss a ball with dog

Still partnered? Get dh to hang with baby while you play with dog

Play 1/2 hour a day alone with dog in 5 minute increments while baby is otherwise occupied

New route for walk to keep things fresher/new toys/treats for dog

Dog park visits to let dog make other friends

Any friends who could play with baby while you do this 1/2 hour with dog?

Some dogs are just this way and it has nothing to do with what you're actually providing the dog, it's just in their nature.

***the United States is one of only four out of 168 countries studied to not have some form of paid family leave for new moms. We join Swaziland, Papua New Guinea, and Lesotho in not having that policy in place. ***