Zebbi, you could have a condition on the running events, something like
Animation "Turning" is Not Playing, that way when you press the key to start turning, the running animation won't interfere with it until it's done.
And you could put another event "On Animation 'Turning' Finshed" - Action - Play "Running" Animation. That way when the turning animation is finished, the running animation starts up and they shouldn't interfere with each other.
Just make sure you don't set the turning animation to loop.