Do you have any ideas for a mare who walks backwards and tries to go back to the barn when you ride her? I'm working with a mare tomorrow and she has been very poorly trained.

I agree with what the others are saying, but because this is an internet forum, we only get a small bit of the story and have no way of properly assessing the horse, so I would also say to check for sensitivity and resistance due to pain. It's most likely a training issue, but it's never any harm to make sure it isn't tack/back/teeth/feet.
As bad as this sounds, you want to make bucking/backing up/standing (anything she does to not go) as terrible as it can be (not anything cruel! but just annoying). Once you ask her to go, if she doesn’t move right away, then to have to constantly kick her, maybe use the aid of a whip, and have your trainer or a friend with a lunge whip lightly tapping her butt. Continue this until she moves forward. As soon as she makes any forward motion (even if it’s just a tiny bit!) stop any nagging you’re doing and let her go. Continue this until she understands that she actually has to move. It will probably take a few lessons but they learn faster than we think! It also sounds like she is getting away with a lot of things so maybe try some groundwork to gain dominance, because it seems like she’s pushing boundaries. I hope this helps and hopefully your mare will behave soon! Best of luck!
This kind of sounds like how my mare was... she probably wants to go back to the barn because she is herdbound. You just have to get her used to being alone, which will take time. But when she starts to back up toward the barn don’t try to pull her forward, but make her really back up. If she is going to back up, she should be running backwards and it’s your choice for that, not hers. She will realize that it’s not worth the work of running backwards and will probably get over it. Backing up is also a sign of submission, so you are now the dominant one.
Another thing you said is that she bucks if you try and make her work. My mare did exactly the same thing. I completely understand and it is so terrible. I don’t know how bad it is for your horse but my horse wouldn’t even go to trot, and sometimes she wouldn’t even walk. I’ll tell you how I got her to listen but I’m not sure if it would work for your horse too depending on how bad it is. So I started by teaching her voice commands. I just did this on the lunge and once she understood that then I knew that if I said “trot” and she didn’t go then it was just her being rude and not a misunderstanding. When you ride and ask her to move, you have to continue. It may take 15 minutes before she moves, but once you’ve started you cannot stop under any circumstances! As soon as you stop, she has “won” and is learning to misbehave. running out of room but continued on another comment!
She's barn sour and probable buddy sour.
Few hints here :
She is easier to ride with a lead horse but when you canter her she is prone to running out of the arena. Without a lead horse she will just buck if you try to make her work
Patience, firmness and time. By making it more unpleasant to go the direction she wants to go, and more pleasant to go to the direction you want her to go. How is she with a lead horse?
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