Question for the electrical guru's here.

I have some things about the electrical in this house that I'm well, less than satisfied with. One of them and the most annoying in the summertime is the circuit for the receptacles in my den and living room. 9 duplex receptacles total. EVERYTHING in this place is wired with 12 gauge copper. I have not found a single run of 14 gauge anywhere and the PO who wired the place assured me there was none. "I don't do no #$%@ work"........

There is a 15 amp breaker on the circuit and if the A/C (window unit) is running and the wife decides to vacuum, then the breaker trips. Do you guys see a problem with swapping it out for a 20 amp breaker? Is there any sort of testing (voltage drop, resistance, etc) I can do to verify ALL the wiring is 12 gauge even where I can't see it? I've not found any illegal hidden junction boxes or the like and the PO was a union electrician by trade (which makes the double tapping in the main panel all the more puzzling.....)

Swapping the breaker (if safe to do so) is my preferred course of action since my other options (in order of preference) are to re-wire the house or re-train the wife.

Hopefully I won't be running window AC units forever, maybe again next season and then I'd like to go with central A/C or split units.