Per Google maps... that's 91 hours and 6,241 miles roundtrip.
Consider going through Las Vegas to Flagstaff and picking up I-40, all the way to Nashville. Be prepared to lay up a couple of days for high winds and/or storm fronts anywhere from Texas on eastward, on that route, regardless of your direction of travel. If you should hit any snow around Flagstaff it won't last long.
Going on down to I-10 would get you out of the wind, generally and maybe out of the worst t-storms in April. Be aware that RV parks on the Gulf Coast have taken a serious beating from hurricanes this year and may be closed due to damage.