first of all, to get your balance better try riding your horse BAREBACK, or with out stirrups.
This will help you to rely mostly on your KNEES to post. Which is what you should be doing.
When you rely on your stirrups you often times don't distribute your weight evenly and ETC.
So try riding with no stirrups and/or bareback for a few rides. Mostly posting [although it will do you wonders to try loping with out stirrups/bareback to help your equitation]
And ALWAYS remember that you need to be UP while your horses inside leg goes up and when that leg goes down, you need to be down. RIGHT on cue.
You can tell a gelding, you can ask a mare, but you must discuss it with a stallion.