Infectious mononucleosis is not as contagious as the flu, since the flu is an airborne pathogen
and can travel greater distances
and spread more rapidly to a wider area.
Mononucleosis, by contrast, is transmitted only through direct contact with the person's saliva. However, you have to remember that your sister-in-law's immune system is depressed because of the chemotherapy, and she is more susceptible to catching pathogens which normal people would be more resistant to.