The solution is to get a bag that the purse will fit in. Yea, there is a slight chance that they will say it is too big, in which case you separate them and check the rollaboard. But in my experience it is a vastly lower chance that a US carrier will complain about the bag size compared to complaining about 3 bags. Someplace like Australia, forget, check a bag, they are very strict. But US carriers you should be fine.

My wife and I went on a RTW a few years ago, and on some trips since took this approach. We had one rollaboard and each had a fairly hefty Briggs and Riley cabin bag of one style or another. She could put her purse in hers and I could put my camera bag in mine as well as quite a bit of other stuff. We flew (in business) on AA, BA, Cathay, Air Vietnam and a few others with no problem. Also, I went to a workshop with a pro photographer at Adorama last year and he talked about traveling with gear and this is the approach he uses more or less. You might search on the travel gear, travel technology and travel photography forums for suggestions on bags to accomplish this and if you dont find what you are looking for try posting there.