History is littered with examples of both of these kingdoms trying to serve the role of the other. That has never worked out. Case in point: the Crusades. When the church takes up the sword, coercion to Christianity happens. That is not the calling of the church. As the late Chuck Colson used to say, “We don’t impose, we propose.” Our role as part of the church is to proclaim the life-giving message of the Gospel of Jesus Christ. We don’t force people to become Christians (unlike Muslims) but we seek to persuade people of the truths of Christianity. As the Holy Spirit works in lives, people come to believe in Christ Jesus. Furthermore, when the earthly kingdom seeks to proclaim the Gospel, they do a poor job of it. Most often secular people trying to be religious boil Christianity down to Law, ignoring the death and resurrection of Jesus.
As Christians, we have callings in each of these kingdoms. In the right hand kingdom (the Church), we are called to receive the good news, praise the Lord, and proclaim that good news to those around us. In the left hand kingdom (the earthly realm), we are called to participate in the process of government by voting, expressing our opinion in the public square, and in general being a "good neighbor.” These two kingdoms are not meant to be separate, as if God rules over one and not the other. They are meant to be understood as distinct. Knowing and understanding that distinction will guide you in how to interact in the midst of both.
If you would like to learn more about the doctrine of the two kingdoms, please let me know. I will point you to some resources for further learning.