Does your mother get SSI (Supplemental Security Income) or does she get Social Security disability benefits? They are not the same thing, but both are paid by the Social Security Administration. If she gets a Form SSA-1099, that's Social Security, not SSI.
Her Social Security benefits, if that's what she's getting, will not be reduced or eliminated if you put her on your medical insurance.
I'm not sure what you mean by "Supplemental, Medical, Medicare." If she is covered by Medicare, why do you want to put her on your insurance?
This is an income tax forum. Your questions are not about income tax. You will get better information if you direct your questions to the Social Security Administration or to an advisor who specializes in Social Security.