To Sleep in the Motel in Fugitives, Kara needs to find dry cloths and 40 Dollars to get her and Alice into the Motel.
How to Sleep in the Motel (Chapter Fugitives)
When you start the chapter Fugitives, go straight ahead and left to check out the motel. Just across from it you find the Laundromat where you can steal cloths from a sleeping person.
Exit the Laundromat, turn right and walk straight until you come to a supermarket that is still open. Use your gun from the previous chapter and steal the money you need for the motel.
You can now check into the motel and spend the night in a warm bed.