Yea all three sides comes off as bad here tbh so i can't see why Lin gets a pass (especially when the main culprit has apparently changed for the better).
You guys are focusing on ONE moment (which to be fair, is the big traumatic moment they choose to have Lin be hung up on). But it wasn't just about her getting scarred. It was about having a parent she couldn't please. It was about her admiring her mom, and wanting to follow in her footsteps and having her mom be disappointed in her for doing this. Her sister pretty much was a terrible person that was given a free reign to do whatever the hell she wanted (even if it meant committing crimes, or causing tension in the family). The fact that Toph supported this (or at least enabled it), while giving Lin a cold shoulder just for wanting to be like her, is a pretty shitty deal.
The reason I think THIS moment specifically was traumatic, was because her mom finally put her foot down and sided with the sister (despite the sisters actions putting a huge blemish on the family's reputation), all while scolding Lin in the process for doing what was right. It's the pivotal moment where Toph finally DOES something, but chooses to help the sister, while making Lin complicit in this corruption (but in a larger sense, allowing the sister to get away with her terrible actions, at the cost of the family -- literally).
I think you have to look at this in a bigger picture kind of way vs. focusing solely on the moment she got a physical scar by her sister. Although it's kind of sad that a huge gash on her face (that she has to carry), was caused by her own flesh and blood. The only problem with Lin, is that she allowed herself to become bitter. She should have let go a long time ago. I don't agree that Lin should have forgiven the sister (especially when the Sister never deserved forgiveness, and never owned up to what she did)...but she shouldn't have let it control her life, to the point she was unable to grow as a person.
Toph and her sister are pretty terrible people.
EDIT: I don't think Lin deserves a pass (to be clear). It was on her to move forward in life, and not allow her shitty family to poison her. But I still feel sympathy for her, and don't really feel any sympathy for the sister or Toph.