I like Amy's answer best; if audited, you will want to show the IRS that you have income related to this trip.
You can only deduct expenses that are directly and reasonably related to work (production of income). That can include actual travel costs, actual lodging costs, and 50% of meals or 50% of the federal meal per diem. Obviously, you can only include your own meals, not your family. And you can't include in your travel, side trips to places that were not work-related. For RV travel, you can't use the standard mileage rate, so you need to use the actual expense method. I suppose your expenses would have been the same with or without the family, including them probably did not increase your transportation cost. For lodging, I suppose you would have to look at what your lodging would have cost if you were traveling alone. (Camp site fees per person or per vehicle? Any nights at hotels, one room or more?)
Just to state again, you can only include expenses that were ordinary and necessary to producing income, and you will need to make some reasonable separation between expenses you would have occurred if making the trip on your own, and expenses that were incurred because you brought your family that were not directly related to producing income.
See here for more. https://www.irs.gov/businesses/small-businesses-self-employed/deducting-business-expenses
