I'm going to preface this with the fact I am cis, but I live in a community of many LGBT kids and know all of their experiences.
One of them is Alex (ftm), and he is still unable to come out. His mother is very conservative, but she reluctantly lets him get his hair cut short and wear baggy clothes.
Another one is Andrew (ftm), and I have no idea how his parents reacted. But they let him go on Testesortone and call him Andrew. So I'm assuming well.
Next, there's Caitlyn (mtf), who's mom took it really well. She smiled and went to buy her daughter some new clothes and makeup. Caitlyn's never been happier then when she wears high heels and lipstick.
Finally, I know Elena (mtf). I knew her before she knew she was transgender. She wore eyeliner sometimes, and got bullied pretty bad for it. Everyone just thought she was edgy or bisexual. Now, a year later, she has the best contour I've ever seen and expensive wigs and dresses. I'm assuming her mother accepts her.
I've never really spoken to them about coming out to their family, but I've experienced coming out to my family as bisexual. I was outted originally to my mother by an ex-friend, but I told my dad. It was a casual thing. I had been commenting about girls casually like, "oh, she's cute" and my parents knew I was a huge supporter of the LGBT community, so when we were talking about the future and I mentioned that I might marry a woman, they weren't surprised. My mom's never outright said it, but she thinks I'm confused, experimenting, and that bisexuality doesn't exist. It's a scary thing. Once you come out, the closet locks shut.
I hope this maybe helped, even if I didn't really answer the question. Keep writing your story. Ask trans people for advice, keep doing that. I wish you the best.