Awesome! I only skipped through bits of the first video, but I like where this is going. He is in your contact now so you can really move away from the stretching frame that you were in before, and more into this working frame. I would still like to see you work to gt more suppleness in the jowel - and he will give it to you, you just need to ask. Ride him at times with much more flexion, and at times straighter. Use your fingers to feel the reins and have a conversation that his mouth does not get dead and dull. As well his neck can come down just slightly, as sometimes he uses the neck as leverage to drop the back.
Now, with your seat, you are sitting very well. However, now that you are sitting with the horse and following him and more able to effectively influence him, it is time to get your body more "in there" and with the motion.
If you watch the video you will see how your body is always a fraction behind the motion - he does a down beat, and then your body does, he does an upbeat, and then your body follows. Think about really tightening your core (sqeezing your body with your upper arm and elbows usually does the trick) and try to ride a bit a head of him, in the sitting trot, actively ride the strides before him, in the canter, riding a half beat faster. Now that you can follow him - you need to tighten up and be with him. Laura Bechtolsheimer dressage training DVDs (TRAILER) - YouTube
I like this video because she is on some younger horses - but you can see how she is in the same body position as you are, but the seat is actively with the horse - she is really undulating her seat and her core is very strong.
This is how you learn to go with the horse, and then any leaps, bucks and bolts become easy to sit because your core is strong and you are moving more with the horse.
Yes it will hurt, a lot at first, but eventually it will become easy. And then I would like to see you ask for more impulsion in the trot.