You are not up there for decorative purposes, you have to ride the horse.
And the time to stop this is before she gets head down, which means you need to be aware of what horse is doing, AND what she is planning to do.
Watch her ears. When a horse's ears move so that one is back and one is forwards? They are thinking and that is a bad thing as they are thinking about doing something they aren't supposed to be doing, such as dropping head, or wandering "accidentally" into tree trunk.
The second you see ears like that, you need to tighten up slightly on reins, kiss to her, or bring calves onto her sides, lightly, and let her know you are wise to her tricks and are not going to tolerate it.
And you will NOT ever win a battle of strength with a horse, you have to out think them, and that means riding proactively, not reactively.
Also, you need to look at your handling mechanics as well, as usually this type of thing goes hand in hand with other problems. Horse snatching lead rope from you to graze when leading, horse fidgeting around when you are grooming, horse showing aggression at feeding.
All those are signs that you are not running the show, the horse is.
Horses make me a better person.