I'm pretty sure $2500 is a felony. It used to be $1000 but since values have increased over the years, the threshold went up.
The theft occurred in Glendale, so yes, they would have had jurisdiction. What they would have needed to prove you had the violin is the serial number. If the one your wife bought had an altered S/N, it would be very suspicious but if the one stolen has a different number from the one she bought, case closed. The store has a record of the serial number, whether they bought it from the distributor, used or took it in trade (there's a card that needs to be filled out for any trades or outright purchases by a pawn shop or retailer). If hey have no record of this instrument, too bad for them.
Probable cause is, to some degree, at the officer's discretion but if they couldn't see it when they looked in the door, they have no right to enter.
FYI- if the police showed up at my door and made claims that didn't seem right, I would call the department and ask to speak with the officer in charge. I would ask the officers for their ID, ask them to step outside while you make the call and don't freak out during the call. The chance of them getting a search warrant in this case would be nil, especially quickly. It's not a big drug or murder case, so there's really no urgency.