No, God is not married.
Man was created twice in Genesis and there is a great deal of metaphor in the Bible's first book. What does Adam's rib symbolize? I don't know, but I suspect that the Adam and Eve of the Garden were non-physical beings representing all of us -- the real us behind these beautiful, Homo sapiens eyes.
Man was created in Genesis 1:26 in the image and likeness of God. But what is that image and likeness? The Ten Commandments caution us not to use graven images. Why? Because God does not have a physical form. Any graven image would thus be a lie. God is a non-physical, spiritual and immortal source of creation. That would make each of us non-physical, spiritual and immortal sources of creation.
Man was created in Genesis 2:7 from the dust of the ground. Dust is not the image and likeness of God. Dust is physical. Dust has form and substance. Could this dust mean chemical elements? Could this man from dust mean Homo sapiens?
It seems from these two passages that man has a dual nature (and perhaps even more complicated). Genesis 6:3 echos this idea stating that God will not always be with man because he is also flesh. If man is also flesh, then he must be something else, too. That something else is the Holy Spirit -- the true self, the immortal soul, the child of God.
Why don't we feel more like children of God?
For one thing, our bodies are a distraction. For another, we have forgotten who we really are, because we were poisoned (individually each of us) by the forbidden fruit of the tree of dichotomies -- good-evil, right-wrong, generous-selfish, compassion-indifference, confidence-doubt -- all elements of ego, the source of all evil.
God does not have gender and neither do His children. Made in His image, we must remember that God is not Homo sapiens. These bodies are a vessel and tool to help us return to Him. Once that mission is accomplished, God will no longer strive with the Homo sapiens species.