You might also consider the lower-drama approach in your contact. (But I think you are right that there should be one final message of some sort.)
Send a message, perhaps via Facebook, and say, "You don't need to worry. The kids and I are fine. But I am taking a long break, so you won't hear from me. Right now I need a lot of space. Don't contact my friends or try to get in touch with me. I'll be back in touch when it feels right for me. The more you harass me, the longer that will be."
Or even something short like, "Mom & Dad--I'm fine and the kids are fine." And nothing more.
With this approach, my idea is that you don't get into proclaiming a huge break. You just remove the whole legitimacy of their "I'm so worried!!!" approach.
Sort of, "don't be a bomb; be Teflon."
"When it feels right for me" could be forever. This declares it as something only you decide.
But that phrase also leaves the door open for highly superficial contact. That hope (false though it may be) might shut them up. And it keeps your sisters out of drama as well.
Once you've sent that, then encourage all of your friends to defriend your mom on Facebook over the next three or four weeks. And do so yourself. And never respond to any of her follow-up questions and pleas.
I had a niece who just up and vanished. There was a showdown about her boyfriend (they were staying w/ her parents; parents said "he can't stay here anymore; you can, but he can't"--it was warranted, believe me). She was mad, of course, but said, "OK, but I'll be the one to tell him," they went for a drive, and they never came back. She didn't call, nothing.
My sister *did* file a missing persons report. But that was because she didn't contact *anybody*--not friends, no one. We were 80% sure she had left on her own, but the 20% chance that she hadn't was real (he'd taken off w/ her in the car before, and she'd called from a rest stop in another state to say, "come get me, I finally was able to get to a phone") made us really worried. And the longer it went on, the more scared we got that his issues had turned violent.
She finally did post something on Facebook that said, "I'm sorry I worried everyone, I'm fine." That one single message had a huge calming effect.
Now, my sister isn't toxic, by any means. And if she'd gotten a message like the one I suggest right away, that would have been an end to it. (Her one single message *did* create an end to it.) Since your parents have driven you away, it's not sensible to compare them.