My horse hates leg cues

I think we really need more information. What sort of training has she got? How long has she been acting this way? Has anything in her diet changed? What skills can you do with her - ground and mounted? What is her diet now? When was her last teeth floating and vet check? Has she ever had a chiropractor or massage therapist?
From what I have been told from her last owner, she has only taught to ride. I had to teach her the leg cues, neck reining and some other stuff. I did have a trainer once that taught me some warm up ground work, and how to turn for barrels (that is what I am training for her to do) When I first got her she wouldn't even let me on bareback and wouldn't go anywhere so she has improved a lot but has always been nipping at my legs. She is still fairly new to the leg cues but know what they mean.
I don't know what her diet was then but now she mainly eats grass and sometimes mixed grass. On the ground she can lunge, back up and I have just taught her to bow and respect others space. She has been doing excellent with ground work.
Mounted she gets a little more fussy about everything. She hates back up but will do it, throws her head around and doesn't respond very well whenever I apply pressure on the bit. My trainer recommended that a vet and chiropractor should look and her teeth and neck. As far as I know, she has never gone to the vet for your teeth and stuff like that.

I agree with the trainer. Get her all checked out just to rule out pain first off.
Sounds like she could be uncertain.
Head tossing with the bit is usually caused by discomfort, so either she is a naturally sensitive horse that balks/ "becomes stubborn" when put into an unpleasant situation & then has little spurts of anger with the biting & bucking, she needs more work on the ground with backing up & moving off of pressure, the bit you are using is too strong, your hands are too heavy for her or she is confused by your aids, in which case she will need more time & work.
It can be any of the above or a combination of several.

Ok so here's a complete list of things to do:
1) get a vet out to do her teeth - if she's never had them done - she needs them at least looked at! Gotta make that happen.
2) get a vet/chiropractor out (it'd be best if you could find someone to do both to avoid two farm calls) to check her neck, back and everything else - even doing a soundness test would be great.
3) get off her back and finish her ground work. It sounds to me like a great deal of building blocks have been skipped and now you're seeing the holes.
In all honesty I'm beginning to think it's a complete lack of training more than a pain thing - she's standing there, kind enough to allow you on her back - then you start kicking/squeezing her - if she has no idea about how to move away from pressure, you're just being a jerk - in her eyes of course.
So here's a list of ground work exercises to work on before getting back on, this will also help establish you as her leader and bring up a few less battles in the future.
a) Backing up - with a halter and lead rope, no other tack, stand in front of her (and a bit to one side so if she spooks you don't get squished o.o) Take a firm step in her direction, with your shoulders square and making firm eye contact, say the word 'back up' at the same time as pushing the lead back behind her chin, applying pressure to the halter's noseband. You want to always start with a tiny amount of pressure, then gradually increase the pressure until she responds. At first she may stand there and ignore it - if she ignores it continue to slowly increase the pressure. She may try turning her head left or right or picking it up or shaking it - just hold steady gentle pressure, don't add more just wait for her to respond correctly. If she gets upset and starts throwing her head around, trying to pull away or gets upset - you used way too much pressure and didn't increase slowly enough. So with gentle pressure, wait, the very split second she starts to just lean back away from you, release the pressure immediately and rub her nose out. Repeat this process over and over again, until she's taking steps back. Do this until you can just take a step into her space and say 'back up' and she will back up a few steps smoothly. You want to see her 'trot' backwards, not clumsily stumble back. Horses naturally back up using diagonal pairs like a trot, so that shows she's comfortable, if she's doing one at a time she's being forced and isn't comfortable, so keep practicing.
b) yielding her hind end - your goal is to make her front end stationary while her hind end circles her front end. To start with you just want her moving away from your pressure, gently apply pressure to the firm, muscular part of her rear end (not the squishy soft part near the spiral, that's very sensitive) - repeat the same sort of concept of pressure as I discussed with backing up - gradually increasing - knowing when is to much, all that. The moment she leans away from your hand release the pressure and rub out the spot, repeat this until she's readily moving her hind end away from the pressure. Once she's doing that you can use the lead rope to help keep her front end stationary, holding her from walking forward and away at the same time. Do this until you can step toward her hind end with your hand raised and she will move away without needing contact.
c) moving the front end away, exactly the same as the hind end, but the front circles the hind. This one is hardest IMO, you apply pressure just behind the point of the shoulder, if she backs up repeatedly you're too far forward, if she goes forward, you're too far back. Find her happy spot and work on this until she's moving around well.
d) Side stepping - now you want all her feet moving sideways. You use the same pressure concepts as all the rest but this time right where your foot would land if you were mounted. In the beginning forward motion is accepted, then you want forward and sideways motions, then eventually you can use the lead rope to prevent forward motion and only ask for sideways motion.
e) put her head down - this skill I always add, it helps shift horses out of flight mode when they get upset, so it's a fantastic skill to keep in your back pocket if you know what I mean ;) This you do by applying pressure in the same ways as always, to her poll. You want to eventually have her drop her nose to the ground with just a soft tug on the lead rope in a downward direction.

Now, if at any point she gets upset or reacts painfully - then this is indeed a pain thing get a vet out! But these are all fantastic and necessary skills for a horse to have. This will teach her the basic understanding of how to move away from pressure - so when you're mounted you will use the same principles with your legs. Gradually increasing the pressure, relieving it immediately when you get a try at the desired response.

So here are the key things to remember:
- immediate release of pressure for even a try at the right thing, they don't know the right thing they're going to try a whole pile of things to figure out which relieves the pressure, so if they even come close reward it! You can fine tune it gradually, once they understand the concept.
- Gradually increase the pressure until they start looking for how to relieve it, when they're looking hold the pressure steady until the accurate response, then immediate release
- Watch for pain and know the difference between painful 'ouch' and disrespect.

Good luck - let me know if you have any questions!