How have some if you made yourself engage your core muscles so you have a better seat when running? I do fine when I'm riding slower but when I run I bounce. I know people suggest riding bareback but my gelding is rough and I don't want to make his back pay for me trying to get a better seat. Any other suggestions? He's very push style and if I don't kick him some and push him he won't go all the way past the barrel so I guess I am not sure how to acheive a good seat and kick. 

Work on your core OFF the horse. You will learn where those muscles are and how to engage them. Tons of beginner core exercises online.

I started doing the Barrel Racer Fit program and it drastically helped me develop my seat, core,  and confidence. It is a definitely a program to ease into or you might not be able to move for a few days but I cannot tell you how much it has helped me. I do the $10/month program and I like that it is all there and I don't have to think about what I need to do. I only do 3 workouts per week so I have some flexability in the workouts I pick since she provides 5 per week.

Did you do her better barrel racer 8 week program to kick start or just start with the weekly deal?

I have only done the monthly service. I actually started a year ago because I bought it during her NFR deal when it was $5 for the first month. I figured for that price it was a worth a try. I am debating trying the Better Barrel Racer 8 week program since it is on sale but haven't decided yet. 

Where do I get info on this program ? I am very interested in it. Thank You 

Her website is barrelracerfit.com/. She also has a FB and instagram.

A person can have strong abdominals but yet not have a strong core because they are missing all the supporting muscle structure strength.  I just went thru a situation (potential hip muscle tear) and I'm happy to say nothing to repair just need to strengthen.  My PT doctor has given me things to do that will help.  I have learned my issue isn't the core strength but those supporting muscle structures...hip flexor, gluteus (minimus and maximus), thigh and hamstring.  Once I get those supporting muscles back in shape my core will be able to work properly and keep me connected to my horse, during a run.  Not sure if that makes sense.

What exercises do thry have you doing? 

Mostly involves a Theraband (big colored elastic band)  and closing them in a door.  Motions that engage the glute and side glute...facing the door and moving leg back,  sideways or turn away from the door and moving leg forward (away from the door).  15 per set and a total of 3 sets.  I do not do them all at once I am not that tough.  I also keep riding with long trotting engaging my core and surrounding support muscles.  Loping circles moving in and out from large to small using leg muscles.  Walking was another option, but I'm not a big down the road walker so that happens just around the barn.  The other thing I was given to do ... laying on your back, bent knees and feet flat on floor then raise hips and hold.  The real test for support muscle strength was this last one and to take one leg (while in the hips raised position) and extend it...haven't been able to do that one yet.  Hope that all makes sense.  I found lots online searching for Hip Strengthing Exercises.