You may be able to deduct the cost for the lodging paid in another state.  To take the deduction for lodging as a business expense, you consider the length of time your spouse spent at each location. You may take the deduction for travel expenses paid or incurred related to a temporary work assignment away from home. However, you cannot deduct travel expenses paid associated with an indefinite work assignment. A work assignment in excess of one year is considered indefinite.

You cannot claim the deduction if your tax home is in the city or location in which you work. Your tax home is the city or general area where your main place of business or work is located, regardless of where you maintain your permanent home.

An example from the IRS Topic. 

"You live with your family in Chicago but work in Milwaukee where you stay in a hotel and eat in restaurants. You return to Chicago every weekend. You may not deduct any of your travel, meals or lodging in Milwaukee because that is your tax home. Your travel on weekends to your family home in Chicago is not for your work, so these expenses are also not deductible. If you regularly work in more than one place, your tax home is the general area where your main place of business or work is located." 

For more information, please visit the IRS topic on Business Travel Expenses.