With all my students in my 35 years of being a professional riding instructor I have yet to see anyone that can actually have a relaxed and soft sitting trot.
Most instructors teach the trot by having the rider trot more . One cannot learn correctness if one is practicing incorrectly. Simple logic!
First the sitting trot is one of the most relaxed and effortless way to ride a horse. Also one should have an effective sitting trot to be able to get a nice smooth canter depart. If the rider does not , the why should the horse give the rider a smooth canter transition?
Start train you and your horse by through doing a nice slow walk. This is done by relaxing your hips so they actually move with the horses back. By learning how to do this your horse will learn how to relax his/her back and be able to swing the horses legs better underneath the horse. When you relax your hips do make sure you are not pinning your knees . Remember relax your lower legs also. Your lower legs should be lightly around the horses barrel. . your entire body should feel like it is jello. You should not have any stiffens in your entire body.
Yes that includes your ankles. Your ankles should feel like they are relaxing down , not being pushed down. (If you are pushing down your ankles to get a deep heel you will be pushing your self off the saddle and not relaxing your hips. ) To simulate the feel of deep relaxed ankles you can stand on steps, with your toes on the step , holding on a railing or something to keep your balance,the slowly allow your ankles to deepen or get lower . Look and see how low the ankles can get while staying comfortable. Are your ankles the same angle as you ride at the walk? If they are good . If not then how do you expect your ankles to be relaxed when you are actually riding ? (Hint... This is also a good exercise to be able to relax and stretch the muscles , tendons and ligaments for riding. )
Getting back to the walk. Now walk on a straight line, or as straight you can walk in a relaxed manner, and tighten or stop your hips from moving . Your horse should slow down , some horses will actually stop . They stop because the horse's natural flow of movement has stopped. Now relax your hips or release your hips . Your horse should walk more fluidly forward . This simple exercise can also be used to slow your horse down instead of using a half halt with your hands or arms.
Now once this relaxation and stiffening or slowing your hips down is accomplished you are ready for the next step.
Look at the horses inside shoulder . When the horses inside shoulder is back softly squeeze your inner calf on the horse's side. When the leg starts to move forward slowly release your leg to the relaxed position or as I call it a neutral position of relaxation. Then look at the outside leg and watch when the outside shoulder is back also. now squeeze your outside calf lightly on the horse side and slowly release your calf on the horses side to the neutral position.
With this accomplished now squeeze and release your inside leg when the inside shoulder is back and then squeeze and release the outside shoulder is back. This will create a tempo for the horse to listen to and will start to move a little more forward. The fast the correct tempo (see the above) if the inside and then outside leg the faster the horse will walk forward . If you use to much leg the horse will trot. Be careful not to use too much leg.
Once your legs can find a tempo of slow and then fast and then slow the horse will start listen to the tempos the rider has created.
Now your hands should have light straight line contact with the horse's mouth , Contact should be just the the amount of pressure to hold the reins straight . Squeeze release your inside hand and outside in same tempo of the inside and outside leg . This informs the horse not to trot and will also soften the horse's mouth . This will also start to tell the horse to listen to the tempo of the rider's fingers.
The next step is when the rider is squeeze and releases the riders calf slowly shift your weight to the side you are using your calf. This gets the horse to re balance the horse's stride and engage the inside and outside legs. It will also teach the rider how to re balance the horse and to step side to side softly at the trot.
Most riders only think of the up and down movement of the horse as they bounce around on the horses back . The horse has four different movements at all gaits. Front to back and side to side. It usually is the side to side motion that creates the bouncing on the horse's back.
By now you are probably wondering how the walk,creating the tempo of the horse and stepping will help the sitting trot.
The rider must educate the horse on these aids to best be able to control the trot. I have found the reason why most riders do not have an effective sitting trot is because they are too busy trying to hang on and stay in the saddle.
With the rider's aids of hands , the stepping side to side softly and legs creating a tempo the rider can practice a forward tempo and then a slower tempo until the this can be accomplished easily.
Slowly increase the horse tempo , or speed (not really speed but length of stride) , at the walk until the horse "accidentally" starts a slow trot . Just sit to the trot a few strides and slow the tempo down with the riders hands , slow stepping and legs . The rider may need to take a little more contact on the horse's mouth to slow or downward transition into the walk.
Notice I have not ever spoken about a transition much , There is one piece for the walk trot transition I have left out. That will be gone over once the slow sitting trot is accomplished.
Make sure once at the trot the rider only trots a few strides . Once a few strides are easy, for the horse and rider team, then keep the forward tempo maybe 2 more strides. Then slow the horse again by slowing the tempo , using all the correct aids . Do this until it is again easy for the team.
If at any time this becomes difficult then go back to the start of the article and practice again from the beginning. One or both of the team members did not get the memo of listening to the tempo.
Once the rider can take a few more slow steps then go a little further . Do not get carried away and do this until you fail. If you do this then the team will need to go back to the start of the article and re learn the correct steps.
This takes as long as it takes to stay slow , calm , quiet and relaxed of both horse and rider team.
Do not rush this !
Once you can accomplish this slowly then increase the tempo slowly again for a few steps. So go a little more forward / faster and slow the horse . Do this until you can do a relaxed slow or forward sitting trot.
In summary create a tempo in conjunction with the horses legs. The tempo is found by using the rider's aids of inside and outside squeeze and release of the rider's calf , inside and out side stepping and inside and outside squeeze and release of the fingers . Make sure the contact of the reins are only the amount of holding the reins straight not tight or pulling/holding.
This is the foundation of all the movements of dressage or as I call it correct riding.
Ride and train well