Can you give us a cite on the original verse?
This is a puzzling question. There must be quite a bit of play in the translation - my NRSV is pretty similar to your translation:
“God, who is enthroned from of old, will hear, and will humble them - because they do not change, and do not fear God.”
On the other hand, the NAB does seem to bear a relation to the other verse:
"God will give me freedom and peace from those who war against me, though there are many who oppose me."