For those who are just joining us
, Petunia gets a howler in OotP that says "REMEMBER MY LAST, PETUNIA" and I think the "last" referred to is a letter written by Dumbledore to Petunia after the third event of the Triwizard Tournament. I forgot who said it wasn't, and they referred to the first letter we know of that Dumbledore gave the Dursleys, the night Harry was dropped off at their house, and that McGonagall says that a letter wouldn't be able to explain it all. This is how I think things went down.............................. 8)
K, It's late, I'm sleepy, hyper, and not-that-smart when I'm sleepy and hyper at the same time, but I'll try to make a reasonable post...
The letter I was talking about wasn't the letter Dumbledore dropped off in P/SS. I don't think he stuck around afterwards, but really, I think Petunia has been in some contact with the wizarding world before P/SS, and a lot more since then. The first chapter is told through Vernon's point of view. I don't think he had any communication with the wizarding world, and I don't think he knew she had been keeping up with it...
But this propounds on my whole theory that, if I'm wrong, I'm going to have to reread the books again to get a general idea of the basic storyline because it's SO in depth:
1. Petunia and Lily's parents were squibs, not muggles.
2. Petunia was jealous of Lily because she's a muggle/squib (I'm a bit confused about the actual name of what Petunia is... the squib daughter of squibs)
3. Petunia meets and marries Vernon, who would hate all things magical, so therefore, she pretends to hate (with good reason) all things magical. BTW, I don't think she likes magical things, just doesn't have the hatred Vernon does.
4. Petunia does keep up with her family secretly (because Vernon doesn't approve)
5. James and Lily die, Voldy flees, Harry needs a home. Dumbledore is able to pawn him off with only a letter, because he knows Petunia's at least kept up with things a little bit, and has the general background.
6. Dumbledore and Petunia keep up a secret (to everyone else, including Harry) corrospondance for the next ten years, but it's been a minimal corrospondance. You know, maybe once a year, Dumbledore would send an owl to her to say "I want to find out how Harry is, make sure you're keeping him safe, remind you of what you have to do."
7. Harry goes off to Hogwarts, first year. Corrospondance ceases, until the very beginning of Chamber of Secrets, when Dumbledore sends an owl to the Dursleys over the flying car mishap.
8. Next corrospondance probably happens around the time of Sirius's escape (keep in mind, Vernon has only received the original Hogwarts letter and the note home to the family in CoS).
9. Harry blows up Aunt Bulldog, more magical folk come into the picture to fix her, the Dursleys say they want Harry to stay at Hogwarts til next summer. I think Dumbledore probably tells Petunia at some point in the year what all is going on with Sirius, or else I think that was one of his original corrospondances with her.
10. Harry goes BACK to Privet Drive, diets with Fatty and Family, the Weasleys blow up the living room and ton-tongue Dudley. Harry goes off to have a great time at the World Cup. I think Petunia probably gets a note regarding the Death Mark and what happened after the World Cup.
11. They get to Hogwarts, fourth year. Weird thing happens. Harry is chosen as the fourth contestant in the Tri-Wizard tournament. Petunia probably gets a letter, since this is weird, and probably Dumbledore and Sirius both realize the potential danger.
12. Harry gets through the first two tasks, no problemo, the Dursleys don't ask and don't care. The Dursleys get invited to and turn down the third event.
13. Crazy stuff happens the night of the third task. Petunia gets a letter (the letter I think is Dumbledore's "last" from the howler) saying basically that Harry just went through this major MAJOR ordeal, saw a fellow-student killed, saw the death eaters, saw Voldy come back to life. Voldy's out and about, the Durlsey's need to keep a tighter reign on Harry now that the main enemy is back. Harry, the Dursleys, and really the rest of mankind is in grave danger, and it's up to Vernon and Petunia to keep Harry extra-safe.
According to my theory, Petunia exchanges notes (and I'm not talking about long sweet detailed epistles, mostly just Dumbledore checking up on her and Harry, and her pert replies) with Dumbledore a number of times in the 15 years we've seen so far. Vernon has known about only about five of them (the letter when Harry was left, the original Hogwarts letter, the letter telling them about the flying car incident, the letter inviting them to the third task, and the howler).
I've checked and double-checked, and there's really no reason my theory can't work, I don't think... we see of Petunia what Vernon or Harry sees of Petunia, but then we thought Moody was the good teacher in book 4, we thought Sirius was the bad guy in book 3, because the story is only told through Harry's eyes... I think the only reason Petunia acts like she HATES (instead of just dislikes) the wizarding race is because she knows Vernon wouldn't stand for it.
And now, it's much more late (that took longer to type than I thought it would!!!
) and I'm even more sleepy, but not as hyper, so it's almost time for the resident crazy person to go night-night. 
doublecheck me, though!
