I have used all 3 options for travel when bird hunting.
For years, I stayed in hotel in Iowa that had "dog" rooms. The place closed down a few years ago.
In the fall, I like to stay in my 21' travel trailer, either at a campground with shore power or remote camping/boondocking. Late fall, with long periods of below freezing temps, I do not use the water systems on the trailer.
When remote camping, the electrical and water systems are good for about 3 days.
The trailer was originally purchased for family vacations so the hunting with it is a bonus.
It is not inexpensive to tow a trailer, but it is nice to stay in my own bed and fix my own food.
When we hunt in January, we rent an Airbnb. It is comfortable and affordable.
I have contemplated building a teardrop camper that could be towed with a small vehicle and would comfortably house me and the dog.