I'd definitely agree with ensuring there's a game plan in place that you're aware of, but remember be flexible.
Is the trainer keeping you in the loop? I'd expect updates even just a quick text. I know I have no issues sending a 30 second text.
Ie Good ride today he's starting to really get the neck reining. Although there was a plastic bag that was going to eat him and he couldn't possibly walk past!
Yes, I know exactly what's going on. I've watched him work with my horse before and I go out and take lessons with the trainer and see my horse every weekend. :)
Some horses need more time than others - but I don't think it should take 3 weeks. With everything I have trained my horses - it has only taken a week at the maximum. But like I said - some horses need a little more time than others.
But I would have to add my personal opinion and disagree with your trainer - it shouldn't take four months.
His training will take awhile because he was green to begin with, and he's learning a whole new method of riding style. He was really cowboyed at his old owner before me, and now he's being trained for western pleasure.