First thing, always ride with a helmet. Especially on a young horse.
As for sitting the trot, that's a VERY important skill. B/c bouncing around on their back at a trot is really hard on the horse - that's how some horses get swayed backs. :/ Anyways, get comfortable at the trot on your horse. There are two ways (well, three if you count two point) to ride at the trot; posting and sitting. Posting is easier because all you do is go up and down (on the correct diagonal, of course).
So make sure your comfortable w/ posting. Sitting the trot is simply tucking your hips with each stride of the back legs. Tuck
deep and even. It takes an advanced rider to sit the trot at a working gait, so you will want to start at a very slow trot. Make sure you have
control of your mare while your learning. Preferably you could find somebody to lunge her, with you on her back w/ a saddle. You def will want to have a helmet on while lunging, for your arms will not be holding the reins, you will just be concentrating on your seat.
The person who is lunging her has to know what they're doing - but I trust your a good enough rider to control the horse on the lunge line, the only reason the lunge line is there is to keep her from bolting away from you; because as I stated before, you will be concentrating mostly on your seat. But that doesn't mean your legs won't be active in controlling her; outside leg behind the girth (keep light on the aids b/c your on the lunge line, no kicking only pushing) inside leg at the girth. Keep your hips active and tucking, no matter how hard you don't want to. Keep your hips tucking with her stride. Keep her slow, almost at a walk..then increase the speed as you can sit it more.
Pretty soon you should remove the stirrups and (yes, yes, it burns but people will be impressed later b/c you took the effort to do this), and practice posting, two point, and sitting the trot. Do this as much as possible.
Ans walla, you can sit the trot!