I really agree with Sailingfool. But from another perspective entirely; I'd say you did not have rip control of the helm away from your GF. You were aware of everything going on around you but for some reason you didn't react in a calm way by just explaining to your GF; That, when other boats are in sight it is always best to anticipate the worse case and take action long before it has to become a "who should do what or not" situation. then show and allow her to take the appropriate action.
I completely understand your point Denise; but please understand that this was a situation where I did not feel comfortable with anyone else at the helm but myself (the boat owner). I don't care if it was a guy, gal, or someone with more helm experience. If boats are going to collide; I would rather be the sole person responsible and thereby protect the liability of my crew.
The situation required rounding up head to wind without being backed in 20 kts and current. I know for a fact that my girlfriend does not have the proper experience to do this. She was being "challenged" enough to begin with; at my discretion/teaching and she was doing great with the boat dipping the rail in on puffs. Technically I should have taken the helm earlier when I became aware of the second crossing situation; but I wanted to let her drive and learn more about who has right-of-way, and why.
She was asking about both boats and I reminded her that we were leeward of the boat to starboard; and the boat on port was also give-way; and in both situations we were required to hold course unless we wanted to become give-way to both boats. What I was trying to get her to realize was that unless the boat is leeward and on starboard and we are bearing down on them; we were not give-way (aside from an anchored boat or overtaking, etc.).
I agree that given a 2 boat situation; we should (and would) have tacked away sooner; with her at the helm. The problem was we had a 3'rd boat closing on our quarter and doing so would have put us on another collision course; and us as the burdened vessel. I would not want anyone else helming that one for the potential for collision either. This was not an issue of gender or dis-trust of her actual abilities. I simply did not want the collision to be due to anything other than a port tack boat not keeping clear of us; by removing her from the equation of "who was driving and why didn't you take control of the situation?".
This is a great thread. Thanks for all of the responses and different opinions; you guys are great. I think you guys are right about different saling venues. I would not feel uncomfortable dipping below another boat with less than a boat length in light wind. Our situation was in heavy air with a high closing speed and that's why I got nervous about the oncoming boat with sprit and kids on their bow. We could not see the cockpit/helmsman; they were behind a dodger and sails as the boat was on a reach. Wind was too high and distances to safely turn were too great to yell instead of using the air horn. My single blast was to get their attention; and there was no reply. Next time it will be followed by 5 blasts instead of one. On other occasions a single blast was followed by an immediate course correction; and thank-you wave for giving them a head's up. I never blast the horn if I can make eye contact and am comfortable in the assumption the burdened vessel is going to stay clear.