Claim the food.
Go in with the hay in one hand and the whip in the other. The whip should be down. Not held up in defense.
If she is at the gate, wave the whip and "kiss" or cluck to her to tell her to back off the gate to give you space. Claim that gate. Claim the space.
Think of it this way, when you go to the grocery store and come back out with your grocery bags, heading to your car, you have a natural sense of "My car." Same as when you park in your driveway and head toward your front door, you have a natural sense of "my house."
Feel strongly about your paddock. Your hay. The same way. Not in a negative way, but say to yourself: "this is mine."
With that, spank the gate, flicker the whip in the air to get the mare to back off from the gate.
When she starts to back off, put the whip back in neutral, pointed to the ground.
Enter when she is backed off enough. Any time she steps in ONE step toward the gate again, stop entering and flicker the whip in the air, "kiss" to her (or cluck, doesn't matter. The noise is the light pressure you'll use later on as a cue by itself without the whip to tell her to move)
So...when the space around the gate is clear and she's staying respectively away and waiting. Then step in.
Walk to wherever it is you set the hay down. Keep the whip down in neutral.
Any time she takes one step toward you, immediately raise the whip and "kiss" or cluck and flick the whip in the air, while looking at her shoulder or chest. Don't look her in the eye. If you tell the body to move, the rest of the horse goes with it, and eye contact can be deemed as aggresiveness.
The moment she moves away, the whip goes back to neutral.
So...point is,....only raise the whip and flick it when she moves forward toward you and the hay. Get as loud as necessary, but don't start loud.
When she moves forward toward you start with just the kiss/cluck sound and look at the shoulder or chest and tell that body part to move away by flicking the whip a bit, then louder then louder still, until you are really making a big commotion and if needed, walking a bit toward her (just a step or two. Because if she doesn't move at all, then you'll make contact with her shoulder, her hip, chest, etc to let her know you are serious)
The moment she moves away, leave her alone.
So...you're in the paddock and she's staying back. Doesn't move at all toward you or the food....now set the food down at your feet. And stand there for a few seconds.
Then kiss to her to invite her in. Look at the hip, to drive it forward. Be quiet about it, not a lot of commotion.
If she walks up and at any time pins her ears, immediately go to high pressure by making a big commotion with the whip. Soon as she backs off, leave her alone. Don't chase after her, just don't let her come near you with ears pinned.
If she walks up with ears forward, head low, quiet and no tension in the body, allow her to come in toward the food. Sidestep if you wish, but don't back off, don't back up. Stand there, let her eat while you're standing there.
Her body is not tense, her ears are up and not pinned and she looks calm and quiet, then leave (don't turn your back on her) sidestep and walk out sidestepping, not turning your back on her (can't trust her yet)
Then walk up casually and if she shows signs of tension, shoo her away instantly. The moment she moves off, stop all pressure. Then invite her back in with a good attitude (on her part)
The point is...she's trying to claim the food because there has been a time when she pinned her ears or whatever...at a person, and that person backed off. So, she thinks she needs to be dominant toward all people.
You're not punishing her. You're just telling her that you are the dominant one not her (in a good way). AND you are also teaching her to move off pressure. And that if she respects the pressure, the pressure will go away.
Soon you both get into a routine of this, she'll understand that she's to be respectful and never try to claim the food and run you off.
Then you can use the use the whip less and less and the kiss/cluck sound more often and then you can eventually phase out the whip altogether. Be sure to use the sound first before you raise the whip, so she can memorize the pattern of what you're asking.
There's 2 problems here:
1. She tries to claim the food and run off anyone else around her
2. She doesn't give to pressure well, because she doesn't understand it as she should. So, applying this lesson in steps, you'll be teaching her that she can find a release of pressure not by rearing or all that stuff but by simply moving her feet. She moves, she gets a release of pressure.