The car has returned to us. A long 54 days later, and it once again graces its appointed parking spot behind our house. We actually parked the other car in the spot during the day, so that our neighbor would get the hint not to straddle the line anymore. It worked, although their car is now parked perilously close to our $7,360.75 repair job.
The happy news is that the long delays by both the insurance company and the repair shop resulted in reductions of our $1000 deductible by $765.52. Basically, that accident cost us $234.48 (+ 54 days, a killer bruise, and some emotional turmoil).