UPDATE 2

Things have completely escalated, and honestly, reading through your comments made me realize waiting around for a deadline was pointless.
On Tuesday, my dad came over to my place to try and "reason with me." By "reason," I mean he spent an hour crying on my couch, telling me that paying $3,500 for the restoration would mean pulling money straight out of Lily’s wedding fund. He admitted Karen threatened to leave him if he paid for it, and he literally begged me to just accept $500 in cash and "let it go for the sake of the family." I told him absolutely not and showed him the door.
Then yesterday, things took an absolute turn. Lily’s fiancé, "Mark," reached out to me directly. Mark was furious because Lily had told him I willingly let Karen take the dress to get altered for her. When he saw how bad things were getting and realized Karen had tricked me into handing it over under the guise of "dry cleaning," they got into a massive fight. Mark told her he’s reconsidering the wedding if she doesn't take accountability and help fix this.
Karen lost her mind and sent me a string of unhinged voice notes accusing me of "destroying her daughter's relationship" and being evil and spiteful.
That was the final straw. I knew right then they were never going to pay a dime to fix the dress and were just trying to manipulate me.
Yesterday afternoon, I met with a local attorney who looked over my mom’s probate records, the before/after photos, and the texts where Karen admitted she took the dress to a tailor under false pretenses after I handed it to her for cleaning. My lawyer confirmed I have a rock-solid case for both civil litigation and grand larceny/property destruction given the dress's value and the damage done.
Directly after leaving my lawyer's office yesterday evening, I walked straight into the police station and filed an official report against Karen.
My dad has gone completely radio silent, and Karen is panicking now that law enforcement is actually involved. My hands are still shaking from the stress of it all, but I’m finally standing my ground. I’ll keep you guys posted on what happens next with the police and court.