“Stop fighting! We’re gonna swerve and wind up on the side of the road,” sounds more natural. “Land” doesn’t seem like a strong enough word and also implies that the car might be momentarily airborne. And “side road” is confusing - do you mean the side of the road, or a different road, like a wrong turn? If the latter, you might say, “we’re gonna swerve and veer off down that side road!” “Drive well,” makes sense, but doesn’t sound natural to me. You might say, “Drive safely!” or “Drive better!” Something more common would be, “Keep your eyes on the road!”

"Stop fighting! or we're gonna swerve and land on the side of the road."