Dance is very central to Jewish expression of happiness. It expresses the way a person connects and relates to God and is central to the joyous moments of the year such as dancing at weddings. As the Talmud teaches, “How do we dance in front of the bride?” — which teaches us to dance and sing at a wedding in a manner that increases the happiness of the newlyweds.
However, dance is not a part of the prayer services in general. There is a widespread custom to dance with a Torah Scroll on when dedicating a new one to a Synagogue. This is based on the source that you cite in The Book of Samuel (II 6:16) where King David danced with great joy when bringing the Ark up into “the City of David”, which is today part of modern Jerusalem.
There is a Festival day in the year called “Simchat Torah” (“Happiness of the Torah”) when each community celebrates the completion of the yearly Torah Reading cycle and begins it again from “In the Beginning”. On that day the community takes out all the Torah Scrolls they have and dance with them for many hours, night and day. It is a sign of our extreme joy that we have the Torah and that our life with the Torah is eternal and never-ending.