If you have comprehensive coverage for your car, your auto insurer is probably the primary responsible carrier. I would submit the claim to them. If they don't pay, then I would submit the claim to the neighbor's homeowner's policy. I don't know what your homeowner's policy says, but I there may be an exclusion since it's your car.
Best of luck.
The first attorney was correct. Submit this to your auto insurer, which ought to cover it. If there is a problem, submit this to your neighbor's homeowner's insurer. Between the two, you should get covered.