I'm an ocean away Down Under in Australia. But I'll be able to go to Texas in late March...I can drive there by car & stay in a hotel room for $20 per night.

Unfortunately, it's not YOUR Texas but OUR Texas. Texas is the name of a town in my state of Queensland. It's actually in the middle of a wonderful area to visit...& one of the activities is going on a camel safari.
Texas is in the middle of farming & grazing land where everybody travels with an Australian Cattle Dog or a Border Collie or a Kelpie in the back of their ute (pick-up). So I think the hotel-motel would have accommodation for dogs.
Go to: http://seq.worldtourism.com.au/RoyalHotelTexas/
And if I drive 1 hr north along the coast before turning south-west to Texas, I can visit the real home of the Crocodile Man that you see on TV. Don't think I'll take the dogs in there!
But, seriously, I hope you all figure out plans for a wonderful visit to YOUR Texas.
Marie