Just slapping straight bars on a road bike isn't going to change your posture. It would be similar to just riding on the tops of your drop bars. You'd need to change the rest of the front end (stem height and angle). That could affect handling (for the good or not). It may be impossible for you to get sufficiently upright and still reach the bars, because of the road bike geometry.

It would be helpful if you could describe what you have trouble doing and why you feel uneasy on the road bike versus the other. Is it just the more responsive feel of the road bike, or do you feel unstable turning, or can you physically not relax for some reason (e.g., support your own weight over your seat)? Something else?