I would also consider rehoming her rather than making her an outside dog just because she sheds.
The pulling out in handfulls... I think it probably can go either way here. You may have a health issue with the dog, or the dog has normal shedding for a golden/lab mix (both breeds are shedders, and I understand that labs may shed more than goldens) and you are simply noticing it more because you are pregnant and it seems worse than ever. Vacuuming twice a day sounds like it might be a bit of the second one. And I'm just saying this because you sound a lot like my sister (normally a neat freak about her house) who went a bit anal when she was preggers both times. Fortunately at the time she didn't have either of her pets yet, because as I remembered she didn't want the dogs near her because of the fur getting on her clothes. She still doesn't like fur on her clothes or on her carpets, but it was at a fever pitch back then.
Shaving her - I don't really get the correlation between that and shedding. The shaved dogs I've met still shed + they are more oily and prone to skin issues than dogs who have a normal coat.
About normal shedding for a golden <- They all are different.
Our first golden rarely to never shed until he got sick. Then it started coming out in clumps, especially on his belly. In his case, he lost his undercoat and it never came back.
Our second golden - I swear he never shed a day in his life. His coat was faulty though for a golden. It was silky.
Our third golden he had an overabundance of coat and definitely it came out in huge clumps all the time. From all the shedding, you would think he would have been BALD, but he always had double the coat of any other golden. We had him checked many times for diabetes and thyroid and kidney issues and anything else we could think of that would be causing the ridiculous shedding and other symptoms. There was nothing wrong with him other than possibly certain allergies. He was a heavy shedder his entire life. <- And 2.5 years after we lost him, I STILL am finding clumps of his fur around the house.
My current guy has a coat very much like our first golden, with minimal shedding. But he HAS had a lot of shedding this winter. It's not coming off in clumps, but he leaves a light layer of fur on my pillow every day that I have to clean off.
^^^ I'm just saying a lot of this is what you deal with and discuss with your vet. If the level of shedding and maintenance is something that you can't physically deal with and there isn't anyone else who is going to love and care for that dog, the best thing for him is to go to a good home where he doesn't have to live outside alone.