I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
If you can prove that they did something to cause the engine to blow, they have to pay to replace the engine. There are two ways to prove that: one is by their own admission, and the other is if you can get an opinion from another mechanic about what caused the engine to blow. The timing is suspicious, but in court it helps to have a bit more so you can prove that, more likely than not, this is their fault.
They have an obligation to put you in the position you'd be in if this hadn't happened, so if you wind up having to sue them, you'll also be able to get reimbursement for loss of use of the vehicle, which tends to work out to $15/day, or for rental of a vehicle similar to yours if you'd prefer to do that. If you need to pay another mechanic to inspect it, that's part of your damages. One option here is to pay them for the new engine, write "under protest" on the check, and then sue for a refund. That's sometimes the fastest way to get your car back.
Usually, your insurance company wouldn't cover a blown engine while driving, but it could be worth talking to them to see what they have to say. Everyone's policy is different. If they do cover it, chances are they'll go after the shop for causing the problem.
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