I decided to vaccinate my older daughter (now 6) after talking to my grandmother about it. I had and still have friends who have chosen not to vaccinate (one because her first child had adverse reactions) and was emotionally distraught trying to decide what to do and weeding through all the articles on the subject (yes- researching). It is really scary to let anything be injected into your baby and feels counter to some natural mothering urges. My grandmother simply said "if you had seen polio, you would not question the benefit of vaccines".
Has your grandmother heard of SV-40, or vaccine-induced polio?
My grandmother had polio as an adult, and recovered with no complications, as did over 99% of people who had polio in the 1940s and 50s. She died several years later from lung cancer as a result of smoking 4 packs a day for 40 years.