So although I do yoga twice a week and karate twice a week, along with running when I can I feel very unstretched for some reason and my right leg doesn't rotate freely like my left one does and I often nearly pull a tendon or soething in my inner thigh when kicking etc.

Perhaps I need to stretch more...? The stretcing we do before training isn't enough in my opinion so on the days I can't get there to do my own warmup in time, we literally stay on one stratch for less than 10 seconds.

Perhaps I'm answering my own quesiton...I'll stretch each day...like a splits stretch and hip stretch or something.

Rotation of the hip is limited by either of 2 things - one you have discussed is due to tight muscles / tendon / ligament, but in some people its bony i.e the position on the femoral head in the acetabulm (hip joint). If it is bony then unfortunately there is not much you can do!