Character Turning Influence

Hello, I am currently creating my own speed-based platformer framework. Everything is working just fine with the exception of the control. Whenever my character is at a stand still, it’s pretty easy to control 'em. When he starts to get up to speed, the controls can hinder the playing experience. What I’m looking for is that whenever the character is at a stand still, the controls remain the same. But when ever I’m holding a dominant direction (i.e. Forward) I’d like the “turning influence” to be turned down. In another example, imagine playing Mario Kart and turning without drifting. If anyone could help me figure this out, I’d really appreciate it. Thank you.