Ideas
I've uploaded them to my gallery (crinrict). I did not try them in a new save though.
Family: Stone
Today I decided to play a new household I had made for testing that has just been sitting there. Still fresh game install that I have not added any mods to. The household could not sing duets together when I took them out for Night on the Town. Both singing skill 3 so should be no problems there. I switched over to my save with your family and the mom and daughter could sing duet together just fine. Switched to my main game save and my two brothers household could not sing duets together.
One thing I will say is when I loaded up the household with the brothers, they were not at home. It showed them to be at the, umm, Starlight Lounge. I think that is the name of it. The karaoke place in San Myshuno that is on the top of a building. Logging in and finding my sims in random places is a new thing and it has been happening a lot. I always put my sims to bed, save, then quit the game or move on to another household. Thought I would mention this and I am going to leave it at that since it is rather off topic and may or may not be pertinent.
Basically the singing duets problem has returned, is not consistent across saves at the same time and is in no way related to mods (that I can see). With that said I do not see what more I could test. It is all above my head now. If there is anything I can do to help expedite a resolution let me know and I'd be happy to oblige.