Since this is basically between you and Anna, I don't think you should involve her family. I know it's because of you that they found out about the nudies, but that's the risk you take by sending such private pictures to another person. If you send a letter, it should be for her. First and foremost, I think she got really hurt that her best friend would be so selfish to move in on a guy you knew she liked so strongly, but I know how it feels when you meet someone, and you just can't help but get closer with eachother. I agree that you should apologize about embarassing her in public. Make sure that she knows that you're not expecting her to forgive you nor respond to your message, but that your means of communication will be open if she should ever feel like it. Even just getting it all off your chest will hopefully give you some closure about this. Also, what's with the "kicking her to the curb" - was that literally or a figure of speech?
I've gone through a similar situation before, so I know how it is. I'm cool with the girl today, I haven't really talked to her in 4 years, but I know she's pregnant with her first kid, so she must be happy :) When she first found out, she got furious and sent a posse after me o____o
It seems like you've given this good thought, so I think you should just go ahead and start writing :) Fortunately, you get more mature the more you age, and since she asks your mom about you, I think there's a chance she would appreciate it.
Also just realised how well our UNs match XD
If you're not comfortable with confronting her directly, don't feel you have to. I think a written letter's a good idea - you can say what you really want to, but you don't have to be face-to-face just yet. You said she talks to your mom - is there any way your mom could maybe give the letter to her? That could work well if your mom could hand the letter directly to her - it might be harder to turn the letter down or throw it away if your mom hands it to her directly instead of getting it in the mail.
And UN is username - Sound and Scream does work pretty well.