The good news is that you was hit in the rear on (opposite) sides, but once the 2nd insurance gets an estimate, they (may) subtract out (some) of the damages from the (1st) hit, (if) both require you rear bumper needs to be replaced, or if (any) part/labor is part of each hit. .
Most likely the damages for each was not that much and you was able to drive your vehicle, thus no hurry to get a shop to fix. Now, (if) you had (any) body shop (other) than Infiniti fix, may have it done (prior) to the 2nd accident.
Any body shop can do work just as good as a dealer. But most people think that the dealer does a better job, but many times they charge more. But, insurance will only pay what is reasonable to fix your vehicle, and most likely Infiniti will have to accept that estimate to fix.
So my guess is that once the 2nd insurance realizes you had (prior) damages when an appraiser or any shop writes an estimate, then you will now have both companies disputing how much (each) will pay, so my guess this could take you into 2018, not on 12/23 to get this resolved.
retired auto adjuster