I sympathise, I'm awful at explaining stuff to people, especially stuff that's important to me, like my gender identity. I go bright red and get the shakes, it's really frustrating. My advice is to write down your explanation in a letter and give it to your mother, because that way you can take as much time over the details in it as you want, and it gets the first hurdle out of the way.
Good luck! I hope it goes according to plan. 🙂