Complete ditto to Sorrel. Back to bacis would be a great idea, since it sounds like her previous owners let her get away with everything. Do NOT let her get away with anything. Always "win" every single lesson by holding your request steady and consistent until she gives you the correct response.
Here's a bit more in-depth on the leads.
It is often the easiest to teach leads from a large circle, because they often will naturally pick the correct one up anyway. So we'll talk about left leads, since that seems to be the problem.
Yes, you will want to pick up on the left shoulder, using the left inside rein, ever so slightly so that her head tips in to the left. You want to be able to see the profile of her left eye on her head, but no more than that (or you are picking up on her too much and she is bending too much). The outside right rein is just there for support.
You will keep your left lower leg OFF her completely (to "open" the door to the left). And cue her with your right heel to ask her to transition into the gallop.
Note that you should have already been traveling at the collected and easy trot in the circle. Don't ask for a gallop if you aren't centered and collected at the trot first. Eventually, you will be able to ask for a gallop from a standstill, but easy things first!!
This guys does a great job of explaining how leads work and how you cue for it. And it explains why you use the OUTSIDE leg to cue for a lead, and not the inside leg.
Therefore, since leads require your horse to be sensitive to your legs, of course you need to teach that FIRST before you try leads. Can you sidepass with her? If not, I would teach that first and get her listening to your legs before you try to do leads.
Here's a few good videos on that. eXHorses's Channel - YouTube eXHorses's Channel - YouTube
I like posting videos because I feel if you can SEE what we're talking about, it makes more sense when you try it.