Rt. 7 is a scenic drive with lots of curves, ups, and downs. You'll average 45 mph with a trailer. An alternate scenic but faster drive from I-40 is US 71 south to US 270 east to Hot Springs.
If you want the route with no curves, then I-40 to I-430 to I-30 to US 70 to Hot Springs. No scenery, lots of trucks, but it's interstate. Also quite a bit further, and probably longer in time in spite of the higher speed.
Another nice route to consider is I-40 to US 59 (at Sallisaw, OK) south to Hwy 88 to US 270 to Hot Springs. Maybe try one of these going and another returning.