How long have you been riding this bike? Steering does feel different depending on the geometry of the front end: head tube angle, fork rake, and trail. A steep head tube angle with little trail will feel twitchy, especially at low speed. It should feel stable at high speed but steer nimbly. You may simply prefer a different frame geometry, though you could probably get used to it in time (or has it been long enough already?). I used to switch between 2 bikes with different geometry and it took a month or more to get used to the twitchier bike. A bike built for touring would have a longer wheelbase and more stable steering.

Or perhaps the frame geometry and your size are forcing your handlebars too far behind the front axle. That's a problem you won't overcome.