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Driving 10 hours is, well, nuts. There's a great White Mountain National Forest campground very close to the road up to the train station. Lots of things to do in the area: hiking near the campground; visit the Mt Washinton Hotel; ride the ski lift up the mountain at the Bretton Woods ski area for $5; have dinner at a restaurant called Fabian's near the campground; watch bears raiding the dumpster behind the restaurant; visit the Flume right on route 3. On the first day you can take route 93 up and on the second day you can take 302 east to go home---a scenic drive to North Conway, then 16 south, and then route 25 through the Lakes Region, back to 93 south.
It would be crazy to drive 10 hours and miss all those great things. Don't let the cats hold you hostage. That's why some people have cats instead of dogs: because you CAN leave them home for two or three days and they will be okay. I did that many times when I had a car. They'll keep each other company. If they're hungry they'll eat dry food. They're not going to starve themselves to death to spite you. Sounds like you and your wife need a two-day getaway.