I wouldn't necessarily burn or destroy these diary entries, but I would do my best not to have them out in the open for now.
In my experience - thoughts and feelings change. It's not until you give life to your feelings in the moment that you can heal and move on from whatever you might be feeling in the 'heat of the moment' so to speak.
What I am trying to say is that your sister-in-law may have written that diary entry (or entries) during a time when her feelings were overwhelming and very much in flux. It is in the expression of feelings that they change and mature. If you don't talk about, write about or express your feelings in the moment, they don't change and you can't grow and move on from them.
It is very likely that your SIL wrote out a bunch of stuff and after having a chance to express herself in her own private diary, her feelings probably changed. You can't move on from intense feelings unless you give expression to them, and let them live a bit. Give them some attention and some respect. If there is anything that I've learned, it's that feelings change, and it is not until you allow expression of your feelings (as "bad" as they may seem) that you can then move forward and move on.
Not sure I'm making sense, but it wouldn't surprise me that even though your SIL may have written some "stuff" about certain family members during a tense time she may have been having - once written and expressed - her feelings probably changed for the better, having gotten it out of her system and given free expression and release.
It's important to remember that something written was probably just how she felt for a moment in time, and after having written it - she probably felt a lot better and her feelings probably changed (in a good way) after that. Sometimes you have to blurt out a bunch of awful stuff in order to clear the air and gain clarity.
Goodness knows I've said some terrible things when blurting out a bunch of bottled-up feelings, only to be surprised at how much my feelings change once I give them free expression and a bit of space to exist. I hope this doesn't sound weird - but what I'm trying to say is that sometimes there is a bunch of "ugly" stuff to say before one can even try to get on a bit of an even keel.
It's important to remember that feelings aren't permanent. Whatever your SIL wrote was only in that moment, and it's possible that after having written down and expressed all of her angst about whatever was going on, she felt much better about things and her feelings may have changed for the better.
In this respect, I don't think it's a great idea to zero-in on an entry or three - or make a huge deal out of it. You are right to try and protect her privacy and hopefully you can help your family understand that lots of people say things "in the moment" and that people's feelings are always in flux.
I am sorry for your loss. I hope that the diary entries don't turn out to be a big deal. It's important to remember that people's feelings are always changing, and that what was said on one particular day isn't the whole story at all. It's just the way your sister-in-law felt at the time she wrote it. Having vented her feelings in her own private diary, she may have felt much better about things afterward. Does that make sense?
Hang in there, and again - I am sorry for your loss.