OPO is a slick airport on the whole, there tends not to be queues for security to enter OPO, or if they are they move very quickly. If you were hand baggage only and with boarding passes already printed you could turn up at the airport with under an hour and get through without needing fast track (Green Way). I suspect local residents on the domestic services would not expect to be turning up very early there. For taking your family though Fast Track based just on your Star Gold will probably be allowed, though I don't think guesting is a formal benefit, and I doubt it would make a material difference if they pointed you to main security.

If you leave the Schengen area at OPO then there is a departing passport check. That's 100% consistent everywhere in Schengen. So there would be no passport check at OPO if going to Spain or Sweden, but there would be if going to UK or USA. OPOs passport check can get a bit busy if there is a UK departure and they haven't switched the gates on, but flights know not to leave until everyone is through, it's quite a small area in OPO. There are e-gates that prevent the queues getting too long, but they seem to want a bit of a queue before they do switch them on. USA can use the egates, though not your children.