The families are groups of Qi Organs which all collaborate in a wider overall function. You can read three articles I wrote which describe the three families. Each family consists of four Qi-functions which are two Yin-Yang pairs in two different elements or equally are one Yin-Yin pair and one Yang-Yang pair which are both one of the Six Divisions
1. Yang Ming and Tai Yin article: https://www.seed.org/articles/six-forms-of-touch.pdf
2. Tai Yang and Shao Yin article: https://www.seed.org/articles/joy_divisions.pdf
3. Jue Yin and Shao Yang article: https://seed.org/wp-content/uploads/2019/02/SFT_JueYin_ShaoYang.pdf
As for your question about feeling the organs. It’s not so much another level of sensitivity but of practising. Our sense of our body (interoception) is like listening to an orchestra. It’s all mixed up together and we feel the music but don’t discriminate between the different instruments. What we are trying to do in the Inner Qigong is to use movement, voice, visualisation etc. to highlight the different instruments. For me it’s exactly like learning to listen for the different instruments in an orchestra. If someone points out the Oboe, saying “that’s the instrument that’s playing da-Da-di-Da” then you learn to hear the timbre of the Oboe and then you start to hear it separately within the music. The same with an organ, if you learn to feel how each organ moves with the breathing, then you learn to recognise that quality of sensation and movement within your normal orchestral sense of self.