Okay, let me get this straight - you consider putting a fence between Polly and Titan "cruelty," and yet you are talking about using a cattle prod on Polly and "chasing them around with a whip?" Ummm, something's not quite getting across here.
Polly wants to be the boss mare. She has Little Titan firmly under her hoof, and she's trying to put you there, too. I don't think it's a matter of her liking you or not, she is assuming that she out-ranks you. It may have something to do with your age, I've noticed that my animals relate differently to adults than they do to young people. No matter, she needs to learn to respect you.
First of all, I would be feeding this horse in her stall. She can be as excited as she likes about the food, but won't be able to hurt you (nasty bruise, by the way!) When she charges you in the paddock, she thinks she's running you off from the food. Put her in the stall. If she's nice, she gets fed. If she threatens you, tell her "No!" and leave, with the food. Give her another chance a few minutes later. It may take a while, but she'll get the message about who's really in charge of the feed bucket!
You want to teach this horse to respect you, not to fear you. There is a big difference! One horse disciplines another by kicking or biting, this hurts, but it is something a horse understands. A smack from your hand or a riding crop is rather similar. The shock from a cattle prod is not. She'd "get out of your space" all right, but she might decide your space included anything this side of the county line!! Don't go there.
Have you ever free-lunged a horse before? Have these horses any experience with it? There is a huge difference between free-lunging and just chasing them around with a whip (actually, it can be done without a whip at all.) It's all about putting mental pressure on the horse, and backing it up with physical pressure only as a last resort. You need to know how to increase pressure, how to decrease pressure, and when to do each one. Your body language is much more important than the whip in your hand. Lunging can be a great tool for teaching a horse to listen to you, but you need to do it right. (I wish I could post a link for you to show you what I'm talking about, but I haven't got the hang of that, yet!) If you just go out there and chase them around, without rhyme nor reason, all they will learn is to avoid you. It borders on abuse, and you will make them impossible to catch!
I'd start working on basic ground manners with this horse. That means walk, whoa, back, respecting your space, that sort of thing. I'm sure she already knows this stuff, she just needs to understand that she takes orders from you, not the other way 'round. I'd then move up to lunging her on a line. Minis are small enough, you don't have to have a 20' lunge line. You can lunge them on a long lead, you just have to cover more ground yourself! I'd stick with walk and whoa at first, it's her brain we're exercising at this point. She's learning to listen to you, and they do that better when they aren't tearing around. You can add speed later, first, you need control.
It's a fine line we walk, dealing with animals. You have to be firm enough, that they don't dare cross you, yet soft enough, that they trust you. Good luck with Polly!