I agree with cascanastargazer, this sounds like it could be a respect issue. She can sense you aren't a weathered rider and wants to see what little behavior quirks she can get away with (all of our 24 horses do that with their riders, even customers).
You need to let her know the behavior isn't going to be tolerated. Pushing her, though, could have its limitations; you want to be safe, so don't push her until she's fussing because you just peed her off!
Also, don't worry about hurting her. These are massive animals and it takes a lot more than us (its normally the gear) to hurt them. If you've ever seen horses play, they often get rough. Their "play blows" could shatter us!
Tiny is also correct. Distract her from the behavior. When I'm behind a kicking mare on the trail and I notice she's showing signs of "a kick is coming," I tell her rider to kick her, turn her a little -- anything except stop her (young children ride this horse, so she gets away with a lot).
For Creampuff and Ben I use the "one rein method," using one rein to pull their nose toward me and then I work them in a few circles (not too many, just 3-5). After a time or two they learn that "x action leads to y boredom." The behavior stops. My co-worker got her horse to stop rearing and whirling using this; now tiny 11-year-olds ride him.
However, you lease this horse. Any training you do, check with the owner. Ask if she's had her teeth floated, if you have to. Some of our horses toss their heads when their teeth are bothering them.
When it comes to horses you have to be concise, consistent, and assertive (not abusive, assertive). Think of it this way:
If you don't understand it, your horse won't understand it. That it why you have to be clear in your cues; don't pull back to stop and kick for "go" at the same time, for example (and it's something I see a lot in my pupils).
"Adapt or perish, now as ever, is nature's inexorable imperative." (H.G. Wells)
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