I had a student last week request a 'core awakening' lesson, where we could focus on position and engaging the core while riding. We did a couple of exercises off the horse to 'wake up' her core: some planking, side plank and sitting on the exercise ball to focus on how her core was working all the time to keep her stable. After that, I had her get on the horse for a lunge line lesson. Without stirrups she experimented with sitting the trot - she is very strong and athletic, especially in her legs from other activities that she does - but those leg and hip muscles really wanted to take over when she rode! It was when she was able to recruit her core to do the work that she was able to relax with a long leg, and when I gave her the stirrups back, she was able to keep them more when her core was working.
One thing I've learned from my time with BioRider is that when the correct muscles are strong, those are the ones that 'volunteer' to do the work when your balance is challenged - and that's exactly what you want. This is why I think it's SO critical for riders to cross train. Focus on training the right muscles for riding and you'll be riding easier in no time!