The thing is it doesn't really matter for the number more times she needs to be boostered. The first booster should be done very soon after weaning. As soon as mom is no longer passing along antibodies. The vaccines need to be boostered every 3-4 weeks after that until after the mom's antibodies are no longer affecting the puppy and making the vaccine's antibodies less effective.
Think of the antibodies of the pup as a roller coaster. Every time you booster the pup you climb a hill. The amount of atibodies start to drop within a few days but, it doesn't hit the sam low as the last hill. When you booster the pup you make a steep climb, each peak is a little higher and each drop is less steep and less far. KWIM? BUT, the mom's antibodies also have an affect. They kind of slow down the car near the top of the hill so that it can't go quite as high as it could otherwise. You want the last booster after the mom's antibodies can no longer do this. BUT, if you didn't do any vacccines utnil that late the pup's immunity would constantly drop from the time it was weaned until the first vaccine. Then, to be effective it would still need one booster to make sure the immunity level was high enough. (or you can do titres and find out but, there are issues with that too). Since Bordetella and Rabies do not need boosters they need to be given after mom's antibodies have worn off.
The only thing that not being vaccinated at 6-7 weeks by the puppy producer does is make it so the pup's immunity is lower than if it had gotten vaccinated. That is only true for between the first and second vaccines though. The way immunity and vaccines work is somewhat complicated, I've really simplified it here. (I can't remember all my T-cell and B-cell, cell memory and other immunology right now LOL)