You idea sounds plausible at first; however, you have not even considered where you would park the RV. Most government campgrounds do not have a space for their employees, and again most do not have sewer hook ups. Six months without a sewer hook up will be problematic. You did not indicate for what agency he will be working for, but if it a federal agency, then good luck! Budgetary constraints about eliminated new hires, even seasonals.
If you think you will live in the RV in New York in the winter, think again. It really is not doable, especially for rookies with a child.
The RV washer/dryer is very small, only allowing a few garments at a time. With a family, you will be doing 2 to 3 loads a day every day.