Taking the half-way point quite literally, one area I found that would meet that criteria would be the Land Between the Lakes in Western Kentucky/Northwest Tennessee. There are RV parks of every kind. I am familiar with two Resort State Parks with RV campgrounds in Kentucky and also some really nice COE parks with full hookups. There would be lots of lakeside activities in June.
If you wanted to drive a bit further than your family in North Carolina, another possibility is Lexington, Kentucky at the Kentucky Horse Park. No lake there, but the Bluegrass area is the heart of thoroughbred horse country. Lexington is a large and growing city.
These are two quite different possibilities, but they are near the half-way point and each offers some good opportunities.
