You're into the world of restoration, rather than repair.

Typically a luthier would find such violins as cheaply as possible at auction and restore them and sell them for between £1,500 and £n,000 and you wouldn't know what had cost what. So, if you were buying this violin already restored, it might cost you anywhere between 1,500 and 4,000. One of our seconds has an 18th century English violin that her mother bought for £50 in 1970. Those days are gone.

For $2,000 I'd hope they would disassemble every component, clean and repair each piece and replace whatever needed replacing, such as the fingerboard (the "mites" didn't eat the pegs, it seems - if there's bits of lead in the holes, someone may have used it for air-rifle practice, lol), then put it all back together again and polish it so that it looks like they made it on their bench yesterday. 

$2,000 seems a bit steep, but it may be on target (A guy on another forum has just been quoted £500 for a new cello bridge, but my luthier reshaped my German violin's fingerboard to match that of my French violin and recarved the German bridge to lower the action to equal that of the French violin and charged me £180. Tragically he has now retired with Parkinson's.). But if you took it to a "shop" then they will probably send it off to a luthier for $1,000 of work and then charge a 100% mark-up.

I'd take their valuation with a pinch of salt, as it may just be to lure you in. If I owned it and wanted to play it, I'd assume I had a violin worth $2,000 after paying it. (you don't say how much it cost you to acquire the violin). But I'd probably insure it for 4,000, just in case.

I'd shop around, go to small luthiers with few overheads and get fully itemised quotes for all the work they intended to do. But you'd need to get player-recommendations of the right luthiers to go to.