Are we approaching God because we don't want to sin anymore or because our sin is the reason Jesus was murdered so that we could approach God?

The heart behind the first reason is not a response to the Lord's violent grace. It is to say "I want something (man's approval, self-righteousness, outer purity, a better life ect) and Jesus is the means to that end. Therefore I want Jesus." The other option is to say, "I have sent you to the cross. Jesus you have done a great work to save me from the path I was on. You rescued me before I knew you. I did nothing to warrant your grace. I accept what you have done."

We must understand God chose us BEFORE we chose him. Therefore all our repentance should be in response to Jesus' saving person and work.