What you're describing is not uncommon in older, arthritic animals. At 25 your pony probably has some joint stiffness or arthritis that makes this hard or painful for her.
You can help her out in a number of ways - first, pick up the hind foot and hold it very LOW to the ground, don't crank it up high in the air with a lot of stifle and hock flexion like you would a younger horse. Maybe even let her rest her toe on the ground as you pick out the sole of the foot. Her reaction may be a pain reaction at having to hold a joint flexed in that postion. Second, do place her against a wall or fence so there's something for her to lean or support herself on while you hold one foot up. That will lessen the panicked slamming the foot down when she feels like she's going to fall down.
You may find it's much easier for her to cope after she's moved around and had some exercise. I wouldn't try to pick feet if she's been standing up all night and is stiff; I would let her have some walking and turnout first.
Finally, if the farrier is due to trim her, I would NOT put her up in a stall beforehand and I would give her a little bute or other antiinflammatory to make her more comfortable for trimming.