IMO stay put and don't start out until this severe storm break has worn itself out and moved on
Then get on the road and get started thru the area before the next front
Stay ahead of the next storm front
The best way to avoid trouble, is to be out in front , or following behind, not driving thru it, not stopped and letting it catch you
A day late or two days early is a lot better than being in the storm
If you stay behind the storm watch out for flood waters ahead at rivers and low highway points
Staying ahead means staying on the move, with only short rest breaks, no stopping for visits or camping