I think we are of a similar age and until recently I too used only what I now understand to be my head voice (described by one of my good friends as "sensitive and sweet"). I was unaware there was anything else until I went to one of Dave and Anni's voice workshops and they talked about "head voice" and "chest voice".
After hearing Dave demonstrate how his voice "breaks" at a certain point and then goes up to what he calls his head voice (falsetto?)I had a go at singing in my chest voice (made sure no one could hear me) and the result sounded (to me) awful. Just like you said, an entirely different person seemed to be singing. However, with a bit of practice the range has improved and I have been told that this much more powerful voice sounds quite acceptable. I can now be heard at the back of the room! The range is more limited and the pitch has to be carefully chosen to be able to "sing through" the break in some songs which have a wide range.
Keep practising. I am pleased to have discovered this other voice (whatever it is called). For me it is still early days and I hope with more use I may extend the range by a note or two.
My guess is that yodelling is the ability to flick from the chest voice to the head voice at the point where the natural "break" happens. Anyone know exactly how it's done? (I'd like to be able to do it too!)