Is it legal to 'include the tax' in the nightly price? Kind of the way stores have 'we pay your sales tax' sales where they reduce the cost of the items so that it works out that much less expensive for the customer?
Can you price the room at $114 and in the details of the listing explain that the cost of the lodging is $100 and the tax is $14? Or would your local tax people look at that and claim that you should be collecting tax on $114 and giving them $15.96 so the cost to the guest was $125.96?
I don't know if my suggestion is legal, but it sure would be simple.