Asking family to be vaccinated

Samantha • Semi-professional tiny human wrangler
Ok, so - long story shortish. I am asking close family members to have their flu vaccines and make sure everything is up to date (whooping cough, etc) if they plan on spending intimate time with my baby, cuddles and kisses, etc. I know there are other parents out there that are doing the same. 
My mother is an antivaxxer. She believes they are more harm than good. She doesn't want me to vaccinate my son at all, and she doesn't want me to get flu vaccine or anything else. When I brought up the subject that we are asking close family to be vaccinated, she flipped and said "no way". She is now saying I am blackmailing her. I told her it is her choice; but she needs to respect our choice as parents. I explained my reasonings as well as herd immunity and she says it's all a "sham". 
How would you handle this? If you have family like mine, who refuse to be vaccinated, what sort of contact would you let them have with your child? We aren't currently talking and she has really hurt my feelings. I tried to handle this as tactfully as possible but I am of the opinion she is being incredibly immature, and I don't know what to do next. I feel as though we are at a stand still. 
I wanted my mum to be there for me and supportive but she fights me on everything. From vaccines to telling me I "cannot use wipes on her baby boy because they're toxic". 
Help 😞