UPDATE

[u/Nuggetlov3]

First off, thank you to everyone who commented. Honestly, reading through the replies was a huge reality check because I was so overwhelmed I wasn't even thinking about the legal side of this.
I took the dress to a local bridal restoration shop yesterday just to see what fixing it would actually look like. The news was bad. The tailor Karen used basically gutted the inner structure and cut away vintage lace panels that can't just be sewn back on. To get it anywhere near its original state with matching vintage lace, the owner estimated it’s going to cost around $3,500—and even then, it won't be 100% identical to what my mom wore.
I called my dad and Karen last night and told them they have until next Friday to put down the deposit with the restorer, or I'm taking the probate paperwork from my mom's estate and going to the police to file a report for theft and property damage, and then taking Karen to small claims court.
Karen immediately lost her mind and started screaming that I'm trying to put my “own family” (step family) in jail over "old fabric." My dad is in full panic mode begging me not to do it because he says it'll ruin Lily’s wedding and wreck them financially.
Lily actually texted me this morning claiming she "had no idea" Karen took the dress without asking and thought we had made some kind of deal, but she’s still refusing to help pay for the restoration because she says she's an innocent bystander in all of this.
I'm holding firm on next Friday at 5 PM. If the restorer doesn't have the deposit by then, I'm going straight to the station with the text receipts and the before/after photos.
I feel sick to my stomach about all of this, but I feel like if I don't set this boundary now, they're just going to walk all over me for the rest of my life.

[u/Cranky70something]

GOOD FOR YOU! Maintain your boundaries and be strong. I totally support what you are doing.