Is there any chance you can come clean to your mom and tell her your son needs her right now? I went through benzo withdrawal, so have no experience with opiates, but if you really want to get sober, chewing a half pill to be able to function to the point of somewhat being there for your son may not be the best for your son, or for you.
Benzo withdrawal left me in the hospital for 10 days after a few weeks f spiraling downhill. I surely couldn't take care of myself, let alone a child.
I'm not trying to scare you into using to be able to function, but from what I read about opiate withdrawal, it's that first week that hammers you to the ground.
Taking a few pills every other day could endanger you and your son. Maybe it's time to bite the bullet? Go to a doctor? Get help from family and recovery groups or medical professionals or both?