Your mom said "many people become sick off of Dialysis" - not true. Only very sick people GET dialysis in the first place. It is not as good as having a working kidney, though, so can be limited in its effectiveness. That's why people get kidney transplants when they can, but as there is a limited supply of available donors (save a life, become an organ donor!) so patients can end up on dialysis long-term while they wait. It is not a perfect solution, though.

Dialysis - to put it in simple turns, extracts a patient's blood, and runs it through a series of filters that do the kidney's job, then return it to the patient. A working kidney's main job is to filter out the blood, so things pass from our bodies as urine, for example, rather than building up. The kidney also helps regulate blood pressure and various other hormones and things, so usually a patient is on medications for other things, when they are at the stage where they need dialysis.

I hope this helps you understand. You needn't argue the point with your mother, but you should know the difference!