Ruth, I wrote an entire book on debunking that myth (that God is defined by our actions and can't be in the presence of sin).  The problem is sin, but not in the way you've probably heard. It is about shame and losing site of God's original judgment of good.

http://www.amazon.com/Discovering-God-Imagination-Jonathan-Brink/dp/0615513956

What I find liberating is beginning with God's original reality in creation, that we are all human beings created in the image of God.  Grace is always there because it's within the fabric of creation.  So it allows me to see with love, in spite of what someone believes.