That is not what is presented in the Bible at all. Yes God is the loving Father of those who are His children through the New Birth. But God is the eternal King, and Christ is the eternal King. Therefore His servants will serve Him, not vice versa.
Of the increase of his government and peace there shall be no end, upon the throne of David, and upon his Kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the LORD of hosts will perform this. (Isa 9:7)
I saw in the night visions, and, behold, one like the Son of Man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him. And there was given him dominion, and glory, and a Kingdom, that all people, nations, and languages, should serve him: his dominion is an everlasting dominion, which shall not pass away, and his Kingdom that which shall not be destroyed. (Dan 7:13,14)