Ok, first question.
I have 3 horses now, so I am going to start with them. Our grey mare was barely halter broke- or should I say she would wear a halter that's it- when I got her, full grown and a food aggressive kicker. She is now being ridden, and when she got out recently I could lead her back to the barn with only my arm around her neck, no rope or halters or anything.
Our paint gelding definitely came 'broke', but I fixed him.
I wasn't told, but came to discover, he was stone deaf. I retrained him to touch cues, and he also walked across a feild and busy road back to the barn with only an arm around his neck now. He had the issue you are talkin about locking up and not wanting to move.
My stud colt came wearing a halter, and that's it. But he is only a year and a half, so I haven't roundpenned or worked with him with a saddle yet, but he picks his feet up and gets sprayed with water and we go for long walks now, junk like that. He also was led by only the neck by a stranger, a police officer who stopped to help us.
Then there was our beach pony, abused and with the halter cutting into her head when we got her, and now she is a pampered pet doin pony parties for the nicest guy who works with the masons or something. Then there was other rescues we had that came away far better trained than they were when we got here. I saw too many so-called professionals seriously abusing horses, I rather do my own.
Now, the second question. For one thing, There must be a reason WHY the horse is doin that, your job is to find out why. I don't mean this the way it is going to sound, apologies ahead of time, but if both your horses are doin it I think it mite be something you are doing. Without being there to see what is goin on, I can't really help you. But you need a horses' full cooperation, so you need to find out why. I can't tell you why, without more info. But I can tell you this. If a horse locks up on you, and won't move forward, a quick way to get them moving again is to turn thier heads to one side, and try to get them to step to the side by pulling on them, tryin to get them to shift thier weight to one leg. Once you get them moving PERIOD, g
get them foin in the direction you want. I would suspect that they give other cues before they lock up, other signs of resistance before it reaches that point.
Not a big fan of lunging, btw, if you do it more than about 4 or 5 times, the horse learns to tune you out, plus trotting in small circles alot is very tiring and bad on the horse, if overdone.