My experience was similar to yours, really. We're both from the same country so I'll outright say that there isn't much information out there available to parents, so it's more or less up to us to "educate" them.
When I started my appointments, my doctor told me the case of an FtM who had been there just before me. His parents weren't very supportive at first... however, once the doctors explained what gender identity is and reasoned with them, they became more acceptant. I'm pretty sure that he's now on T!
I can relate to what you said about "realising" things too late. My mom was overwhelmed mostly because she knew I had girlfriends and didn't think I'd be "gay"... I explained to her that it's got very little to do with what I'm attracted to, and more with what I feel like. To her ignorance, I was always bisexual, so she's in for a surprise lol.
Your sister sounds outright ignorant, no offense, and I hope that you can help change her mentality... but I think there's hope with your mom and her reaction. She probably thinks people get "sex changes" overnight because they feel like it, she has to become aware of what gender dysphoria is and what it makes people feel like. Again, educating her is the best course of action you can take! =)
Most parents aren't accepting of things like this right at the start, it takes time. It's hard to process and they'll go through denial, feel like they're losing their child, guilt for "not having been able to tell". It's a major life-changing decision for their children, and it often involves surgeries, so they're always going to be defensive about it, it's really not anyone's fault.
Be strong and patient, you'll work it out. The hardest part's over, you already dropped the bomb, now it's all about sugarcoating your words and making them feel more comfortable with the subject, so that it can be discussed properly. Again, it takes time... don't drop too many things on them at once, they'll need help as much as you do. =)
