And what "part" of the kingdom of God is "the kingdom of heaven"?

Is this not two kingdoms? A kingdom within a kingdom?

I submit to you that the phrase "kingdom of heaven" is a standard 1st century Judaic euphemism for "kingdom of God", much as "The Name" is a modern Jewish euphemism for "God", and much as we today might say "Heaven only knows".

And thus, "kingdom of heaven" and "kingdom of God" are the exact same thing, and no distinction was implied or necessary, except a distinction of emphasis on the heavenly source of God's kingdom.