For some taxes, the business owner is indeed the tax collector. Sales tax, occupancy tax, convenience tax, entertainment tax, arena tax, municipal and regional district tax, Convention and Visitor tax, park fee....all of these are broken out on my bill. I suppose it is bad that my schools taught me to read. Some are a fixed rate, everyone collects the same tax no matter how much the room costs. Some are a percentage and depends on the room cost. The point I'm making is that I pay these when I stay in a room. Every hotel/motel in a taxing location (usually municipality) has to collect these from me. The Hilton doesn't get an advantage compared to the specialty themed hotel a block away.
I'll grant that the Air B&B (or whatever "sharing economy" entity competes with you) does seem to hold an advantage since they don't seem to need to jump through the hoops you need to do, and probably don't collect all these taxes. Maybe you should reopen as Amelia's Air B&B