The idea that they understood it meant sacrificing his son by leaving him behind in a land is also false. How can leaving a son get rewards?
If one is familiar with the story of Abraham in Quran, they will know that he was dedicated to spreading the message of God. Abraham left his son to go further afield and continue this task. We already know from Quran there was a family separation in the story of Abraham.
The reward is related to obeying God's command (and doing good). Abraham was guided, throughout his life, blessed with offspring etc all because he followed and actualised God's command.
You said it yourself:
"Rewards are given for good deeds, following and putting into practice the principles of the Divine Revelation."
Loving one's children more than God or more than enacting what God commands and trying to help and reach as many people as possible etc is not befitting a prophet of God. Abraham passed the test with flying colours.
In any case, if you have checked the actual Arabic and consider QXP's rendition a better fit then there is no problem, each to their own :)