Yes, I would just be "my child, my rules" and make it very clear you will not take any interference on the reading front. Don't be intimidated by the teacher thing - I am a teacher but had to learn - and unlearn - so much when I started home edding.
I don't have research but plenty of anecdotal evidence and that's what changed my mind (which will be hard for you to give to your mum, sorry).
When DD2 came out of school at 8, she was a fantastic reader who had been reading very fluently since reception. We went to various home ed groups, including book clubs, and I'm afraid to say I was a) slightly smug that she was by far the best reader there 
and b) slightly shocked that some of her new friends had apparently made no start on reading at all.
Fast forward to now, all age 13. Her best friend did not start to read until 11 and then seemed to read almost overnight. She wanted to do it, so she did it. She's not the only one - DD2 has two or three other friends who were very late readers and now all read perfectly.
At 8, DD2's best friend could not write her name even. Now they sit and chat on facebook and guess who has the better spelling and grammar? DD's friend writes perfectly, better than most adults, whereas DD still drives me to distraction by confusing too/two/to and there/ their/ they're etc. I think there's a lot to be said for not being turned off of these things by having them rammed down your throat at 5.
I honestly wonder what the point was of infant school and why we put so much emphasis into formal learning at primary age. She could have been playing 
. It's like walking. Some children walk at 9 months, some at 18 months. But once you are an adult no one cares when you learnt to walk and you can't tell who learnt early. I think reading is the same.
Good luck with dealing with this - and stick to your guns. Try to find other like minded people so you have support :)