For so hath the Lord commanded us (houtōs gar entetaltai hēmin ho kurios). Perfect middle indicative of entellō, poetic (Pindar) and late verb to enjoin (Act 1:2). The command of the Lord Paul finds in Isa 49:6 quoted by Simeon also (Luk 2:32). The conviction of Paul’s mind was now made clear by the fact of the rejection by the Jews. He could now see more clearly the words of the prophet about the Gentiles: The Messiah is declared by God in Isaiah to be “a light to the Gentiles” (ethnōn, objective genitive), “a light for revelation to the Gentiles” (phōs eis apokalupsin ethnōn, Luk 2:32). So Paul is carrying out the will of God in turning to the Gentiles. He will still appeal to the Jews elsewhere as they allow him to do so, but not here.
That thou shouldest be (tou einai se). Genitive articular infinitive of purpose with the accusative of general reference. This is all according to God’s fixed purpose (tetheika, perfect active indicative of tithēmi).
Unto the uttermost part of the earth (heōs eschatou tēs gēs). Unto the last portion (genitive neuter, not feminine) of the earth. It is a long time from Paul to now, not to say from Isaiah to now, and not yet has the gospel been carried to half of the people of earth. God’s people are slow in carrying out God’s plans for salvation.