One thing that might be helpful is to think of rearing as one giant no to you. So start examining everything you do with her and don't let her get away with a thing. For you to be an effective leader you need to be consistent.
Rearing is usually caused by a horse wanting to go somewhere the rider doesn't or a lack of forward.
First she needs to be able to flex and disengage her hindquarters. You also need to be able to put pressure on her without her protesting.
To fix this you will be doing a bunch of very basic things so you'll want to be in either a snaffle or a bitless option like a side pull. I also like to have a dressage whip to make sure I have an aid to back up my leg.
At this point you are no where ready to be on the trails, you ned to go back to basics and go to a round pen or the very least arena.
When you start riding, mount with her head tipped toward you and start in roundpen if you can. Then flex each direction. When she will flex without thinking about moving her feet and has her attention on you (pay attention to her ears.). The next step is disengaging her hindquarters. Flex, slide your leg back and press your calf, if she doesn't move back it up with your whip.
It does NOT count if she crosses over behind. If you are disengaging to the left you want the hind left leg to cross over in front of the hind right leg.
An important thing to note that if you are encountering problems do not escalate the pressure, keep it the same or she will likely do the same.
It may be exceedingly boring for a few rides because you will be staying at each step until it's great.
If she won't stand for mounting she is totally out of control at the stand still so why should you go further until that's good? If she can't flex without wanting to move around she's out of control etc. You want the tools to fix your problems before they occur basically and that's what all of these basics do.
Since rearing is a lack of forward, avoid asking for a walk from a standstill. Disengage her hindquarters and have her moving off your leg nice then let her walk out of it by releasing her head. You will be allowing forward while those hinds are still crossed behind so going up won't be an option.
Just practice those few things for the first part of the ride. Flex, disengage then walk around on a loose rein. You're only focusing on forward for now and getting control of her hip so just let her walk around wherever.
You'll see that she will gravitate to a certain area which is fine. Flex her around there and disengage her hindquarter. Use your whip to annoy her, tap, tap, tap on her butt for a few circles. Then when she is pointing away from that area let her walk forward.
You will making the wrong thing hard and the right thing easy. You'll be teaching her to make the right choices without a big rearing fight.
If at any point you're riding around and you notice she is getting anxious and tense bend her around and get her relaxed, the same if she gets distracted.
Again you are NOT steering at this point. Trying to get her to go somewhere at this point can result in a rear. You don't ave a solid base to correct this yet.
When you are walking around relaxed, can flex and disengage then you're ready for trotting.
Cluck, give a squeeze with your legs then a light tap. Do not get progressively harder, just keep the pressure till you get a trot. The INSTANT she offers to speed up, quit. You need to give her a right answer if you keep on her even when she goes there will be no point in her being good.
At this point you are only saying, go when I ask later when THAT is good, when she breaks to a walk, immediately ask again.