Many people can't quit, even with a cancer diagnosis. Heck, my mom kept smoking after her heart attack. It is VERY hard to quit, especially under times of stress - and what's more stressful than cancer?
The 2 things that helped my mom quit were being in the hospital almost 3 weeks where it was impossible to smoke, and the fear that she would rupture her lung tumor by coughing (which was a very real possibility before she got chemo) and bleed to death. Then, she had such a great tumor response, she's inspired to stay quit so she can beat this beast.
Try not to be angry with your mom. It isn't personal. She's likely scared, depressed, in physical pain, and ashamed that she smoked in the first place. Talk to her dr. about medical support to help her quit - antidepressants may be of more help than the patch.