Yes, God certainly does want you to be happy. After all, He made you, and He put within each of us a yearning to be happy. The angel who announced Jesus' birth declared, "I bring you good news of great joy that will be for all the people" (Luke 2:10).
But happiness never comes from ignoring God or seeking happiness apart from His plan for our lives. You see, life is full of choices, and the choices we make will determine the path we'll follow through life. But when we make wrong choices, we end up on wrong paths -- paths that will never give us the happiness we seek. They may promise happiness for a time, but eventually we'll discover it's a lie.
And I'm afraid this is what has happened to you. From what you say, you've spent most of your life going from one relationship to another, hoping you'll eventually find lasting happiness. But you never have, and you never will, as long as you stay on that path.
My prayer is that you will find God's path by turning your life over to Jesus Christ. God loves you; He loves you so much that His Son was willing to give His life for you. Commit your life and your future into His hands, then seek out a church where you can grow spiritually. God's promise is for you: "You will fill me with joy in your presence" (Psalm 16:11).