So many things wrong with this situation that I hardly know where to start. *Sigh* I guess I'll just break it down and take one thing at a time.
First of all, when your mother walked into that bathroom and caught her 12yo daughter masturbating, her one and only response should've been "Sorry" and to then turn right around and FUCKING WALK OUT! No, hell, that's not even the first thing to consider here; the first issue is why the FUCK didn't your mother KNOCK on the door?! It's a matter of common damn courtesy and respect for someone's privacy. I'm all for being comfortable with nudity and all that, but you should at least knock and give someone the opportunity to refuse you entry if they're in their naked.
Ok, so next up, I'm assuming that your mom's response was to just turn around and walk out before she freaked. I assume this because your letter seems to imply that nothing at all has been said to your sister about this. I sincerely HOPE that my assumption is correct and that your mom didn't just flip and start calling your sister a dirty whore or something (I've heard of that happening, seriously).
Third, your mom has absolutely no reason to be freaking out. Obviously you know this, but for the benefit of my other readers who are sometimes not so bright, I think it needs to be stated that masturbation is perfectly normal for anyone of any age. Babies have been observed in utero rubbing themselves. Working with little kids (especially 4 year olds), I have seen more than one just start rubbing themselves spontaneously. Working with mentally challenged kids who don't understand the concept of privacy, I have had the unfortunate experience of seeing more than one young boy "playing with himself." Heh, I remember one who was about 10 who'd wrap himself up in a sleeping bag on the floor and just start going to work on that shit; it was like his own little pleasure cacoon, LOL. And I've heard stories from other teachers about them noticing the activity just in time for the kid to achieve orgasm (we're talking full-on hot sweaty grunting shit here from really young kids). The point of me mentioning all this is to illustrate what intelligent people already know: Masturbation is as much a natural human activity as BREATHING! The only difference is that it makes other people uncomfortable, so it's best to do it in private, which is what your sister was doing, which means that she did NOT ONE DAMN THING wrong!
Your dad kinda had the right idea until your mom hen-pecked his balls away. Personally, I'd have asked my daughter if she wanted a "toy" for Christmas to prevent arthritis... but that's just me, LOL! Anyway, I'm glad to hear that your dad was fine with it, seemingly. At least there's one semi-sane parent in the house. I say "semi" sane because if he were fully sane, he'd have shoved his foot up your mom's ass for being an uptight bitch about the whole thing.
So anyway, let's get down to the real meat of your letter. You need to know how to talk to a 12 year old girl about masturbation. It's very simple: There's NOTHING for you to say to her! The conversation should go like this:
You: Listen, I came in here to talk to you cuz I didn't want mom to do it. She's a retard and she's being stupid about what she saw you doing in the bath the other night. I don't need to tell you anything and we don't need to talk about this, just make sure that if mom asks, you tell her that we talked about it and everything's fine now. Lie to her and tell her you're sorry and you won't do it anymore. Then, be more careful next time. Do that shit in bed at night under the covers, not where our dumbass mom can walk in on you. Ok?
Lil' Sis: Ok.
[you leave the room]
Lil' Sis: Ok.
[you leave the room]
That's IT. All she needs to hear from you is that you're covering for her and she needs to fucking go along with it. You can throw in some sisterly "I'm sorry this is happening, I know it's humiliating" kinda shit too if you want.
Good luck with your little cunt-to-cunt talk.
P.S. - Sorry about not being there anymore. Maybe if I got more questions like this instead of... uh, NOTHING, I could've kept it open. It just seems that, contrary to popular belief, young people aren't all that interested in talking about sex. Feel free to ask your sex questions on The Sniper Forum, though. Everybody who was at EAS is there too and while we're more insane here at SnipeMe, we're still great big fucking know-it-alls about the "facts of life" and we'll still help.