If it is the saddle, is there anything I can do? I tried tilting it downwards in the front by using a corrective pad in the back, but it put so much pressure on her withers that she had a circle on either side where she didn't sweat. So that's concerning to me too. I'm wondering if this new saddle is still too narrow for her, even though my instructor thought it looked fine when I first got it.
No, you don't want to alter the saddle like that because the #1 priority is that it needs to fit your horse's back. With that said, the #2 priority is it needs to fit the rider too!
I'm not as well-versed with dressage saddles but you may need to experiment with different flap lengths, seat depths, and saddle designs. http://www.doversaddlery.com/images/...0selection.pdf
My concern about her size was because, to my eyes, it looks like I am a little hunched up on top of her and sometimes I can feel my feet hitting her elbow/forearm when cantering in a circle or on a turn.
If your legs are in a chair-seat position and way out in front of you, this is going to happen.
Also, are you bracing with your lower leg? This can push your legs into a chair seat as well. Again, this is where doing some stirrup-less work can give you more insight.
Also, make sure your saddle is NOT placed too far forward on your horse's back. Here's some saddle fitting guidelines: https://youtu.be/Ffsz53UwLF0 https://youtu.be/EEIY0iv7ljA
I am also still a beginner rider, so I haven't ever heard of being 'behind the vertical.' But I just looked it up and basically the horse's mouth shouldn't be behind it's poll? What are your suggestions about that?
That's the general gist of it.
But also, head carriage comes from BEHIND .... and shouldn't really come much from the reins. If your horse is traveling in a collected and correct frame, the head/neck should be aligned as well.
Your instructor should be able to help you with this, and help you push your horse forward with your seat and legs, and help you with your rein cues as well, so she's not getting behind the vertical.