"I think we have turned a corner but I'm worried that this will drive another wedge between us all again."
Aim for the best, flatter their niceness and kindness, praise them when they do well and treat children and grandchildren fairly.
That's what I would do, praise the good.
"...something life-changing happened in the past with SIL and I was scapegoated and really hurt by it. I just want everything to be OK between us all, and don't want anything to break the fragile peace we now have. I guess this hurt might actually be fear in disguise."
Did this issue get resolved, if so, move on.
"I am not a bad person, despite what some of these posts have said."
of course you are not bad, lots of people on mumsnet are just nuts and like coing on here and making themselves feel better by being horrible! Don't waste your energy on them.
"Please don't hate me." No one hates you, some posters just like to act in a mean way, it's not about you, it is about them!