Co ordination is a huge factor in your ability to be a balanced and even rider. If you are not then how can you expect your horse to be balanced and even on both sides?
If you have a very dominant side that likes to take over the job of the other hand then doing some simple things with your less dominant hand in everyday life will help you greatly with your coordiantion as a rider. I struggled for a long time to get my left hand to be able to do it's job properly as my right hand was always trying to overtake. So I started to do simple things with my left hand like scoop the feeds in to the buckets, brush my horse with my left hand, brush my teeth with my left hand (yes it was messy and hilarious) etc etc. This worked a treat!!!!
I later found out that what I had done was create new neural pathways for my left hand. This in turn then allowed my left hand to work much easier as there were many more neural pathways for the messages from my brain to my hand now. Interesting hey!
Give it a go and let me know if you see any difference in your coordination with your riding. Happy Riding!