Your sister is correct.
It's all part of desensitizing.
When desensitizing you want to make sure you quit whatever it is you are trying to desensitize the horse to only when he relaxes.
That's when the horse understands that you stop when he relaxes, if you quit when he is all upset, you teach/reinforce that's what it takes to get you to stop.
When you were trying to dismount you were actually teaching him to act that way since you stopped trying to get off when he was getting nervous.
Also, I wanted to mention to you that when you are attempting to mount, pull his head towards you a little bit. Doesn't has to be towards you much.
That's great that you can throw a rope over his back and have him going over a tarp.
I would expand that to being able to throw a rope all over his body: chest, front and back legs girth line, butt, neck. If he moves keep moving with him while still throwing the rope gently around the body part you were working on. Being careful to stay out of the kick zone.
It's extremely helpful to be able to work with your horse as much as you can. But, if you can't you can't, but be prepared for the situation to take longer to get a handle on.
Is there anyway you could get a trainer to come to you once a week for awhile till you feel more confident?
Good luck and I'm glad Major was ok after his little run!