I drove mine back from Vegas, wasn't uncomfortable at all. Though, it was a brand new car at the time (< 10mi).
I still drive long distances in this car and it's not bad at all.
Based on your situation, I'd probably just ship it since you've got a ton of stuff to take with you, but I dunno with the dogs. Maybe rent a U-Haul and trailer to transfer your car and carry your stuff?