We've now done:
just leg kicks holding a kickboard, with head up and with head immersed
just leg kicks with fins, arms straight ahead, hands locked together
some other stuff
leg kicks with fins lying on one side, one arm ahead, breathing the whole time
ditto, with side changes
ditto, with 3 arm strokes and side change
and have now upgraded to the Drill from Hell...
... which is face in the water, regular leg kicks/no fins, one hand flat on a kickboard ahead, one arm doing the arm stroke, and practicing the breathing rhythm: one arm stroke - hold your breath, one more arm stroke - breathe out, twist face up, breathe in.
I hate thsi drill! There's so much to think about, and half the time I bungle the breathing out so I end up trying to breathe in while there's still air in my lungs and the other half of the time I try to breathe in and there's just a helluva lot of water there. 
I made a little bit of progress when I realized that the arm stroke, like in paddling, doesn't generate an even force. There's one point in the stroke where you can feel your arm giving a bit more "shove", which is good to use to start the rotation. But mostly I struggle because I'm used to breathing out the entire time doing breaststroke except when I come up to breathe in, so expelling air fast feels quite strange to me. And holding my breath feels even worse. I read somewhere that the breathing reflex is not connected to needing more oxygen, because there's quite a bit of oxygen left in the air you breathe out, but connected to a build-up of carbon dioxide in your lungs, so you feel the need to breathe out. Whatever the reason, my head feels like it's about to explode.
Owell, keeps my head busy.
Winter riding is much less about badassery and much more about bundle-uppery. - malkin
1995 Kona Cinder Cone commuterFrankenbike/Selle Italia SLR Lady Gel Flow
2008 white Nakamura Summit Custom mtb/Terry Falcon X
2000 Schwinn Fastback Comp road bike/Specialized Jett