If all parties check in online and print off the boarding cards at home that makes life really easy.

The printed boarding card presented at the bag drop will be fine for your parents.

Its no big deal that your parents dont have the CC that the booking was made on. I never have the CC that my bookings are made on!! (I don't & never pay for my flights !!!!!!!!!!)

As for getting your bags checked through from GLA to SFO - I'm not sure...becasue although you are on the same airline you and your wife are completing the journey on 2 tickets. GLA-LHR and then LHR-SFO. But even if you can't...again its no big thing. Just collect your bags at LHR, up in the lift and bag drop them with your parents. I do that a couple of times a year if i'm meeting my Hubby at LHR and then we check in together before going Airside.

Good luck.