I am not a fan of home treatment because I have had a very bad experience with it. I nearly lost my first bunny to a medication allergic-type reaction, and ended up spending over a thousand dollars at the emergency vet, where he stayed for 4+ days at death's door, which was a harrowing experience for me emotionally.
That said, the treatment for syphillis is injection of penicillin G, which can be purchased at most farm supply stores. I am not sure of the dosing, but it should be diluted 1:1 with a sterile saline solution or distilled water. It is a one-time injection that should not need to be repeated and it is relatively easy to do. It is done sub-cutaneously, and you can find videos on how to do sub-q injection on this forum and other places. The skin near the neck is tented and you inject into the layer between the skin and the underlying body wall. Make sure no penicillin leaks out or gets on the fur because it is toxic if taken orally for rabbits.
Naturestee fostered a litter of rabbits that got syphillis from their mother so she would know dosages. You can PM her for that info.
As for the mom, make sure she does not have a prolapsed anus instead of syphillis. Anal prolapse is not uncommon in rabbits--basically the very end gets turned inside out so you see a very angry red area of skin around the anus. It usually can be pushed back in if it is a prolapse, but cannot if it is syphillis. If it is a prolapse the only treatment will require vet intervention--stitches are usually needed from what I understand.
