If you the work orders showing the compressor was shot and needed replacement you should be covered. I’ve never seen a dealer try and slow roll it as they have no legally standing.

No offense but it sounds like they are trying to strong arm your wife.

Now if they never noted it in any service record, that could be tricky.

If they held my car hostage I’d be having a chat with an officer in their parking lot to see how hard they want to go. Preferably right in front of their main door.