it's waste of money to appeal. if CBP bring the denial, just explain to them.
highly unlikely u are going to have issue. there's couple of people i knew went outside US for over 2 years, came back with GC that still valid, the CBP person only grumbled a little but then said "welcome back" and let her in
like u said, u are going back soon, so just come back soon with ur family. there's no "safer" POE, it really depend which officer you got, not state/city specific. officer might have bad day, good day, who knows