She is a cutie! Smaller than the mare I have that mimics her behavior--Havannah is 15.3--but almost the same color.
As for assertiveness: I, too, have a hard time projecting my intent to both Havannah and Athene, my Lusitano filly. One thing that I discovered that might work for you, too, is carrying a short version of the lead I use on my rope halters. When I work my mares in-hand, with the halter, I use the popper-end of the lead to smack the ground when I want their attention. I don't hit THEM, but the ground. The sound and motion of whacking the dirt startles them and gets their eyes on ME and what I'm asking for. I did the same thing one day when I was riding Athene after working her in-hand: the halter was under her bridle and I had the lead in my hand. If I wanted her to pay attention to me, for any reason, I'd smack my leg/boot with the popper end of the lead. That worked well: she knows what the pop means--eyes center, girl, I'm talking to you--and she recognized it as being the same thing when I whacked my leg. Or my boot, or the saddle pad, or the stirrup iron.
I had a 4' long lead rope made with a popper on one end and a wrist strap on the other end. That way I can carry my "back up" without needing a halter/lead crowding everything. I carried it Sunday when I rode Havannah away from the barn--she's buddy/barn sour--and that day I got her the farthest from the barn that I've been able to do so far.
A friend of mine--who's a gifted natural horsemanship trainer--was able to ride Havannah quite a ways from the barn without problems b/c she can project her authority to horses, but Havannah is still refusing to work like that for me b/c I can't do it yet. But, on Sunday, having that short rope not only gave her a cue she knew--the pop--it made me feel more assertive, more sure of myself. Between the pop and my new assertiveness, she was able to see me as more of a leader.
Maybe that's what you need to make you feel more in charge, a back-up. If YOU feel it, your mare will feel it, also. The rope/popper is not made to punish the mare, but to get her focussed on YOU: without her attention, you'll get nothing from her. If she thinks she's all alone, being the leader herself, she's spooky and unsure. She NEEDS you to be the leader, she feels safer that way.
It sounds like what the trainer told you: get assertive. I was amazed by what a "back-up" would do for my feeling of being in charge. I highly recommend it.