There's quite a few very different things going on...
Your original question - YABVU. Regardless of youe plans, your message said, very loudly and clearly - you are not important enough for me to take under a minute out of my day to txt and ask if we're still having our call. It's not like you had to wait for the reply. IMO, I was thoughtless and hurtful.
Your sister, however, is also BU. To refuse to even engage seems immature.
And this shines a light in the next point. It sounds like your upbringing and family life have had major impact on both of you. Instead of supporting one another, you seem to take it out on one other. You describe her terribly - bullying, aggressive, selfish etc, however you seem to thrive on being the victim, even though you're not, however much yiu think you are. You take some responsibility and blame whilst not really believing it - even if you've blinded yourself to this. You say horrible, nasty bitchy things about your sister and in the next breath give reason for such behaviour. If you really believed it, you'd refrain from character bashing her.
You did a shitty thing. Own it. Fix it. Or don't But coming on a public forum to openly paint a negative pic of your sibling says so much more than what you're actually saying
You could call her via WhatsApp when you take the children to their activities - or do you need to be 100% part of those? You could call her via WhatsApp on the way to meeting your friends /going to and coming home from work. Relationships aren't tit for tat. Either you want it or you don't.
Trying to justify the thoughtless thing you did by annihilating your sister's character is low. Very
I'll get blasted for saying this but it's MN so to be expected.
Send her a heartfelt apology letter (only if you mean it - sincerely, though). Writing it down means you can tweak and make it true to what you really want to say - and be honest. Tell her (as non confrontationally as possible) how her behaviour impacts you. Arrange some flowers/chocs /booze/home goodies to be delivered (whichever she'll appreciate most). Do what you can to fix it and, if you can't - at least you'll know for sure you did everything you could without the need to turn to social media for justification.
I hope it all works out - it really sounds like you both need each other and could benefit one another if you were more open, honest and supportive with one another. It's a long hard journey but worth it