frequency of trips
No, it makes no sense to spend any money on a RV. Since you only have 3 weeks and a couple of weekends (during the hottest time of the year), any RV you buy will end up costing you 1000's of dollars per night, so you would be better off staying in fancy hotels. Don't forget that an RV costs to use (larger gas usage, park rental) and even when you don't use it (storage, depreciation, maintenance and registration/insurance).
What an RV will not do, is limit how much you can use it. Only the person who allows you 3 weeks and a few weekends this year, and no freedom at all in future years, can answer the question of how often you can use a trailer...
Considering you are so constrained, Chelse's rental suggestion is a good one.