Do we need a VISA for Beijing or may we travel in the 72 hour window?

My mother and I are Canadian Citizens wanting to travel from Japan to Taipei to Beijing for 3 days and back to Japan. I am currently on a work type in Japan, she is visiting me from Canada. Also, if we leave Beijing within the 72 hour window, but we have a layover in Shanghai, is that counted as part of the 72 hours, or is it acceptable?
Thank you.