Weather will be warm. Mid-April is the normal last frost date in Tennessee and you will be further south. You could easily move into early or mid- March for a start date.
Biggest weather issue could be thunderstorms/rain. Do make sure you have some way to stay aware of LOCAL watches/warnings. If there is a tornado warning, get OUT of the RV and into a substantial building.
Bring your antihistamines.
It's hard to say what is a not-to-miss thing--that totally depends on what you like. Dollywood is nice but Great Smokey Mountains National Park is THE thing to do in TN/NC.
IMHO the only thing to do in Atlanta is figure out the best way to avoid it.
If you like historic stuff, there is tons of it in TN and Georgia. The area around Chattanooga is beautiful in the spring and lots of interesting stuff to see.