I believe the cure for doublemindedness would be total surrender--of the sin--of our will. Surrender, submission to God; repentance. Growth teaches dependence on God and not ourselves.
Being doubleminded is a struggle, in that we know what God desires and in these fraile human bodies, we struggle to release control of our own lives totally to Him; maybe it's pride, maybe fear is the issue, and maybe it's patience--or should I say impatience.... Whatever the issue is for each of us individually, when we fail the test in seeking His will first, we have the assurance that when we go before Him in sincere humility, with confession of our sin, He is just and righteous to forgive us.
Praise Him for His love and faithfulness to forgive our weaknesses.