Just a different perspective here and I am honestly not trying to cause issues...
I agree she is being unreasonable about the coat. Does she feel the altercation itself was handled properly? I understand your child is a child and made a bad choice. The thing is, it seems your son would have had to push him pretty hard or be pretty physical to rip his coat and that would anger me as a mom if it wasn't being addressed. I just wonder if maybe she's making a big deal out of the jacket because she's angry about the incident itself.
It's not the route I would take, but I do have a child who has been hurt and the "boys will be boys" attitude is kind of infuriating. I am just wondering if all the other stuff has been addressed (punishment, apologies for trying to hurt him). If it has.. carry on. If it hasn't.. maybe that will calm her down a little?
Thanks for pointing this out... Maybe... when I met with the Principal, he actually told me not to be too hard on my son over this thing.
My son apologized to the other boy and served detention in school for the incident. He's grounded at home. And she knew it was his money that I was offering to her.

(not b/c of your kid, but b/c of how you respond to it)This sounds like kids were playing rough,like kids do sometimes,and something got ripped. Happens all the time with the kids who play in my yard. Anyone who sends their kid to my house in 'vanity' clothes rather than clothes the kid can be comfortable in, learns quickly not to do it again. Most kids go home from our place muddy at the very least(hello new shoes lol) sometimes with a scraped knee(hello bandaid collection) and if something gets torn while playing I let the parents (friends of mine) know that kids play,and I encourage playing. Lots of active playing. I would NEVER ask another parent to fund my kids clothing collection,and I wouldn't expect to be blamed for when the kids rip their clothes in a game of tag.
the only games where kids don't ruin clothes are video games where they're staring blankfaced at a screen from a chair for hours on end...I'll take the damage to clothes anyday in place of that......
Did they mark your backpack somehow?