Moving a horse when the objective is to get it to stand still, is not something I am into.
Horses are moving when you go to mount because you are letting them, may also be toeing horse, or using reins to lever up. Don't know as am not there to watch you.
But, teaching a horse a "be still" command is something I'd work on, you an use that command, park out, plant those feet, stay, or whatever works for you, but begin with, every single time, and I mean every single time, you halter and lead, bridle and lead, or walk into stall of pen and get horse caught up, STAND STILL...no talking, not patting, nothing, just you standing still, not looking at horse, and if horse moves, give your chosen command, and then just stand there.
When you are leading, stop and just stand still, facing same way as horse is, NO talking or chatting or petting, just stand there until YOU decide to move. If horse fidgets, tell it to be still, or growl low in throat, and then stand some more.
I also cue for back every time I am working with a horse that is antsy to handle, and periodically with one well trained too.
I teach back up with facing horse off to side slightly, horse should be haltered for you all, safer, me, I do it either way. But halter/lead in right hand, facing rear of horse, and with left hand on area where noseband falls, LIGHTLY...push against nose, using slight downwards motion, you want horse breaking at poll, not nose up. And quietly say "back", if horse resists, increase pressure a very slight little, and "rock" nose to chest...*you are not trying to touch nose to brisket* but a gentle rocking motion, and say back.
ONLY increase pressure if horse is resistant, and the very instant you get a backwards shift off of front end, to begin moving back, let up some on nose pressure, but continue to ask for back. Get a step at least, more are fine, but you do not want to just go to backing willy nilly here.
And remember, light as you can, feather touch at first, in all things.
This will get horse used to coming back off of nose pressure, which will transfer to bit/reins too.
I halter and then back horse before coming out of stalls, and will also just stand there, even in middle of coming out. This reinforces in horse's mind that you make the decisions, not them.
You may also need a taller mounting block too. And slightly shorten offside rein, so that if horse should move, hindquarters are coming under you, instead of swinging away. Make sure you are not toeing, and that you aren't plopping down in saddle, nor are you dragging leg over rump.
While I am firm believer in horse should get used to you not tiptoeing around it, at this point, you are too new to this to be not looking at your techniques as a possible problem.
Also, make sure you are not babying horse, nor using a "soothing" tone...as in It'sssss allllll rigggghhhhhttttt method of horse handling, that will turn one into a fool very quickly. Horses respond best to quiet, calm commands in no nonsense voice.
Horses make me a better person.