Adjective : an indulgent parent.    From Dictionary.com. 

As the non-indulgent parent did not observe Tom's name in the papers, his little deception was never found out, and he continued doing duty for his club in this way for a couple of seasons.    From Wordnik.com.  [Scottish Football Reminiscences and Sketches] Reference

My strict, non-indulgent parents ... well, they disappeared a few years ago, to be replaced with these two marshmallows bobbing in a sea of warm grandparently chocolately goodness.    From Wordnik.com.  [The Journey] Reference