How exciting!
I don’t think there is too much value in having the carriers side by side. The idea with the stress is that they will snuggle together for comfort. Some people like to bring the new bun home in the same carrier as the other, but I’ve always preferred to just let the new bun settle in a bit before launching into things. I think people usually opt to do the car ride home together when they are planning to just marathon them straight through, like if they are getting two new un-bonded buns, so the whole home is neutral.
If you do opt to do some car rides at some point (I’ve always found them helpful), I prefer to use a large plastic bin over a carrier. Then have a helper drive, and you sit in the back with the buns. The bin allows you to easily prevent any fighting or nipping. I think with my last pair I eventually switched to using a carrier once I knew they wouldn’t fight in the car.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.