The star quarterback and Shailene Woodley were spotted touching down in Oahu on Monday ... all while Rodgers' problems with the Packers continue to rage on.

But, it doesn't seem like the couple took any of that emotional baggage with them ... 'cause the two looked happy as hell hoppin' off the private jet and receiving their fresh leis!

Rodgers was all smiles ... dappin' up people on the tarmac and handing out hugs.

Of course, back in Green Bay -- it's a whole lot more stressful ... 'cause the Packers are trying like hell to get Rodgers to come back and quarterback their team.

Rodgers, though, has remained upset over his contract situation and some of the team's personnel moves ... and has reportedly already decided he doesn't want to play for Pack anymore.

Green Bay officials have insisted they won't let that happen ... declining trade offers and promising to try to meet all of Rodgers' demands by the start of the season in Sept.

In fact, head coach Matt LaFleur just told reporters last week "we want [Rodgers] back in the worst way."

Unclear if that'll happen ... but if it does go down -- we're sure Aaron's going to have the best tan in Wisconsin at this point!

By the way ... Rodgers and Woodley have been inseparable since the two announced their engagement earlier this year -- we've now seen them in Canada, Mexico, Disney World and Hawaii.