Well, there are plenty of folks in our 50's and behond who can relate to your emotional state there. I get fearful when the horse I ride is afraid. Along with the great advice to ride out with other people, if you have some chances to just ride in the arena or round pen to build on your seat. Part of being ok with side passes or sudden movements is knowing that you won't come off just from that. If you have a strong enough seat, you won't worry too much about those things, you'll just accept them the same way you accept the weather. Horses do move around a lot in unpredictable ways, but usually it's just a step or too, and they stop. Shying scares me a lot, but 99% of the time, I don't come off and it's over in a milisecond and the world goes on and nothing bad happens. If you can have a strong enough seat, from riding in the arena and literally strengthening your legs and core muscles, you will feel less apt to stress the small stuff.
Your being less panicked about small, unexpected movements will translate to your mare as you being confident overall. When you ride with the horse throught a spook, and just keep going, the horse feels less threatened by your lack of balance than if you grip like a leach.
I know, easier said than done. But the stronger you can be physically, and the more accepting you can be of the smaller, sudden sideways movements (without gripping or yanking on the mouth) the more your horse will trust YOU.