As others have suggested----3 to 4 weeks is a very limited period of time for the trip you are planning. Generally speaking:
1. travel time-- most(not all) RVers only travel about 300 to 400 miles per day and/or 5 hrs. per day. When you go beyond these times or miles you will gradually feel some negative wear and tear on your body and general moods. 4 people in 1 RV can become tense and stressful on relationships.
2. Reservations----Look at your travel agenda for the trip and try to make as many reservations in advance as you can. Nothing worse than pulling into a strange town and begin a search for a RV park at the end of a long day driving. Reservations are not ball and chains, you always cancel or reschedule a reservation.
3. Strongly suggest a "Emergency Road Side Service" plan in the event of break downs i.e. blow out a tire, dead battery, RV won't start etc etc.
4. Tires--- if your tires are 4 yrs. or more old---throw them away and put some LT tires with "E", "G" or heavier tires on. Your tires may look like they have good thread left but after 4 to 5 yrs. you pushing your luck!!!!
5. Make a list of the most desired places to see/visit for each person and then rank them in terms of priority for each person.
6. Check the weather conditions each day before you start. iPhone, Lap top, weather radio, CB radio for weather conditions and for road information/conditions from 18 wheelers i.e. accidents ahead of you, possible alternate routes if road ahead is blocked.
enjoy your trip:)