Reminds me of the trip we took moving our DD and her cat to NJ. Suburban pulling a U-Haul trailer loaded to the gills. We hit a bad storm heading north out of Hagerstown on 81 and it was raining so hard you couldn't even see the road. Got to Harrisburg area, still raining, and I was pooped (about 11:00 pm) and so we abandoned plans to drive straight thru to NJ, and decided to stop. Of course some classic car show is in town and all the motels are booked! Used an app on my phone to find a hotel, I even forget what brand it was. They had a few rooms left. Get to the lobby and there is a giant sign on the wall behind the front desk that says "NO PETS"...ugh!
I check in, park around back, and carry the cat carrier in the side door with a blanket over it. Locked the cat in the bathroom so if there was an accident at least it would be tile and not carpet. Turned out all was OK, but certainly a story for the archives....
Best of luck on your move and trip!