Well, I tried it again. This time I connected both USB cables and then opened one IDE window. It reset both micro boards once at this point.
I selected the USB for the Duemilanove and loaded a sketch for that target. Both boards reset again.
So I compiled and loaded the sketch to the '2009' board. Then I clicked on the 'Serial Monitor' icon. It reset both boards again.
So it has nothing to do with having multiple IDEs or multiple sketches opened at the same time.
Maybe it is in the version of AVRdude or some other low level piece of the system.
I use one '2009' to test the other '2009' and every time this reset buggers up the tests.