I can't help with your specific questions, but if it's any help in planning, we average just about 50 mph when travelling on major highways, and that's with a travelling speed usually between 60-65, unless the speed limit is lower. So, with a 2,500 mile trip, that's just about 50 hours of driving. Keep in mind, though, that 50 mph was for our family and, at most, two medium size dogs, and included periodic stops for restroom use, walking the dogs, refills on drinks, snacks, sandwiches & refueling. But, it's going to take you A LOT longer to walk 13 dogs, so I'm guessing your average travelling speed will probably be closer to 45 mph, maybe even less, pushing the total driving time to a minimum of 56 hours. Plus, we only had one vehicle to refuel, you'll have to coordinate refueling for up to 4 vehicles. That will slow down your average a bit, as well. But there's NO WAY you'll average 60 mph or even 55 mph.
I think you should plan on the 45 mph average. If you should average better than that, then call it a night early and try to hit the road a bit earlier the next day. Or if there's a person available to make calls, see if you can find an alternate site for the night.
Speaking of which, will there be additional passengers NOT driving in any of the vehicles? It would be extremely helpful if there was at least one person NOT driving that could make calls or tend to miscellaneous tasks which might come up.
Driving 10 hours with a 45 mph average means 450 miles per day. You might try to find suitable locations at distances of 400, 450 & 500 miles from the previous night to give you some flexibility. That would allow you to make adjustments "on the fly" if you should either be ahead of schedule, or behind schedule.
Another thing I just thought of is the days get short at that time of year. I'd plan on arriving at your destination in the daylight and leaving VERY EARLY in the morning. I find it a lot easier to LEAVE a (campground) parking area in the dark than arriving at one in the dark. Seeing as you'll have to get the dogs walked and settled, I would think you'd need at least 30-60 minutes BEFORE it gets dark. It could just be me, but I HATE trying to figure out the "lay of the land" in the dark.
Google Maps quickly shows two routes: one more northerly on I-80 and another southern route on I-40. I'm assuming you're planning on taking the more southerly route to (hopefully) eliminate the chance of freezing precipitation.
This sounds like a very challenging logistics question. Please keep us updated on your ideas as well as let us know how it all worked out for you.
Good Luck,
~Rick
2005 Georgie Boy Cruise Master 3625 DS on a Workhorse W-22
Rick, Gail, 1 girl (27-Angel since 2008), 1 girl (22), 2 boys (23 & 20).
2001 Honda Odyssey, Demco Aluminator tow bar & tow plate, SMI Silent Partner brake controller.