Multi-part question

I decided on a horse to lease, and am so excited. Her name is Jesse, the 8 year old QH mare. She's such a love: comes in from pasture when you call her name, drops her head if you lightly touch her poll, and is honestly the most responsive horse I've ever ridden. Last night I went through the whole process with her (verus them already having her tacked up the 1st time I came to ride), and they suggested I lunge her first because she's only been ridden 3 times this winter/spring. She did fine to the left, and definitely had some crazies to work out. She walked, trotted and cantered, with a couple of hops and bucks in there as well. However, when I went to work her in the opposite direction (and she was a little tired from the heat and work), she just kept walking toward me. No matter what I did, she wouldn't move in the opposite direction. Thoughts/suggestions?

Secondly: None of the tack in their barn was bought specifically with Jesse in mind. She's kinda rolly polly right now after not being worked through the winter, plus she's just a stout QH girl. They *think* their Western saddle fits her best, so that's what I've used. I'm not convinced it fits her right, because she's fine cantering on the lunge line, and definitely moves out under saddle at the walk and trot, but when I ask for a canter she rolls her back and does a hop-stop. How can I determine if it's a tack issue and not possibly my faulty riding? I paid close attention to my seat and hands as I was sitting the trot before asking for the canter, and I don't think I was doing anything differently. I also didn't let her anticipate the canter by doing a lot of walk-trot transitions when I felt her speeding up.

Your first question: Don't give up. Make the circle small if you need to, use a lunge whip if you need to, just make her work the other way :)

Your second question(s): Some horses are more responsive than others to ill-fitting tack. The canter/lope is the only a-symmetrical gait (3 beats versus 2 or 4), so if tack is not the proper fit, the canter can amplify these effects.
My friend spent 6 months searching for a saddle; her mare was very very picky - sometimes all you had to do was put the saddle on and her ears would go back and her tail would be going! But with saddles she tolerated being on her, she would be fine with them at the walk and trot, but if it didn't fit well, she exploded at the canter.
In the long run, tack that doesn't fit can lead to lameness or injury, which isn't good.
I would strongly suggest getting a certified saddle fitter out to see what's going on :)
Best of luck!

Thanks JDI! How on earth does one go about finding a certified saddle fitter? I was thinking of buying my own saddle soon anyway, because I want an all-purpose English saddle for more close contact, and just the way she's built made me think she would need her own well-fitted saddle.

I'll get some videos/pictures up next week of my riding so you guys can help me make sure it's nothing about my riding that's triggering this.

Phone around to your local tack shops, they might know of someone that is an expert saddle fitter :) I came upon mine by accident; I was shopping for a new saddle at a tack store and they approached me about getting a saddle professionally fit; after getting an idea about her body type, the saddle fitter came out to my barn with different saddles for me to try, and explained exactly what she looked for in the right fit.
Hope I helped a little..?

There's a huge tack shop in my city; I can give them a call and see if they can recommend anyone. I'm fine working her at the walk/trot in the interim (and saddle), and I want to do some good groundwork with her too, because she has a lot of Parelli training under her belt.

On top of what's already been said...

Keep in mind that she's very out shape and it's going to take some time for her to get conditioned again. She might be sore, she might be lazy, she might just not be used to working. When you were lunging and she kept coming towards you it sounds like that's her weaker side and she just didn't feel like working anymore. Keep her moving best you can and use a lunge whip if you need one. With a horse that keeps stopping and facing me I tap them on the shoulder with the stick part of it starting lightly and getting harder until they move away from it. Remember to walk towards them as if you're "pushing" them away from you with your body when you want them to move. Eventually she'll get the point and realize she's supposed to keep moving.

It's hard to say whether or not the cantering issue is tack related without seeing/feeling the saddle and watching her go. Could be. Is there any more padding you could add underneath it to see if anything's pinching her? I know almost nothing about fitting western saddles. :) But keep in mind that before you make a big investment in a new saddle you may want to wait until she takes some of the weight off first. The shape of their back may slightly change as she loses weight and you want the saddle to fit to her "normal" back. Are there any other saddles you could just try just to see what happens? Is there anyone at your barn who can watch you and tell you if you're doing something strange at the canter? Is there any chance you're hitting her in the mouth? Is she sore backed at all? (press your fingers on her spine and see if she flinches) Just other things to consider if it's not a tack issue!

As others mentioned, when a horse comes in to you while lunging, he wants to quit. When our mares do this, I just walk them back out to the circle edge and start again (no praise, nothing). They'll get the message that they're not finished yet.

This is all so helpful.

Yea, I know she definitely need some conditioning to get back into shape. I had forgotten about moving toward her to move her away from me; I just kept trying to direct her with the whip and moving away from her. I'll try that.

I used a "squishy" pad (according to the owner) and a regular blanket under the saddle. I asked my friend who was watching if I was doing anything like hanging on her mouth. I can ask the owner's daughter to watch though and see what she thinks. She has an all-purpose English saddle I could try, though Jesse has mainly been trained Western. Other than that, all they have is a pony's Western saddle.

Perhaps the cantering issue is not a tack but training issue? Just a thought. Or it could be just her being naughty - especially if she hasn't been ridden much lately.

I would recommend get a saddle fitter to come out and fit her. I get all my horses fit. Call your local tack store and have them come out and do it for you.