He set aside the existing royal concessions to the Jews, secured through John the father of Eupolemus: The existing royal concessions to the Jews refers to special privileges granted the Jews by King Antiochus~III (223–187 b.c.), not a number of Syrian kings as Good News Bible and Contemporary English Version suggest. For Eupolemus see 1Macc 8.17.
Who went on the mission to establish friendship and alliance with the Romans: For friendship and alliance, see 1Macc 8.17; 12.3, 16; 14.18; 15.17. This whole relative clause refers to Eupolemus, not to his father John. Making this clear is the principal translational problem in the verse. Good News Bible solves it well with a sentence in parentheses. Another model that does this for the first half of this verse is “He abolished the special privileges [or, favors] that John, father of Eupolemus, had persuaded the Syrian king to give to the Jews. (Eupolemus later went to Rome to secure the friendship and support of the Romans.)” However, in languages that do not use parentheses, translators may say “He did away with our rights that John, the father of Eupolumus, had persuaded the Syrian king to give to the Jews. Eupolemus was the messenger who later went to the Romans and made them our friends and allies” (similarly Contemporary English Version).
And he destroyed the lawful ways of living and introduced new customs contrary to the law: It will be good to begin a new sentence here and to clarify that the pronoun he refers to Jason (so Good News Bible). The lawful ways of living refers to living according to the Torah, the Law of Moses. The new customs were the Greek customs contrary to Torah and Jewish tradition. Good News Bible may serve as a reliable model for the last half of this verse. Another possibility is “Jason put an end to [or, destroyed] our Jewish way of life and introduced new customs that were contrary to our Law.”
Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on 1-2 Maccabees. (UBS Helps for Translators). New York: UBS, 2011. For this and other handbooks for translators see here.