Long-time lurker, currently not riding due to retired horse… feeling like making sure I remember some riding basics…
Your hands should be as far apart as the width of your horse’s mouth, generally about 5 inches. I don’t know if your trainer is telling you to THINK it’s 2 inches because your hands keep widening (or maybe they mean about 2 inches higher than the wither? so you remember to bend your elbows).
I did not learn the “box” idea, but you can take a short crop and hold it between your thumbs (parallel to your body, across/over the withers), after you have gathered up your reins, to keep your hands from drifting, so you get a feel for where they should be (as wide as the horse’s mouth), in addition to marking your reins so you know what length those should be also (so you know where your elbows ought to be). With the crop held that way, it also prevents you from dropping your hands below the neck, though they can still be too low.
Or if I turn I tend to drop the one rein significantly lower (again totally without realizing) and my trainer says I drop my hands to the side of my horses neck instead of keeping them forward and right on top of the mane. I understand these are all wrong, but I was wondering if someone can explain what exactly it does? I also have a tendency to cross my reins. I also know terrible and is usually a lack of inside leg (I am working on it I promise haha). I am just interested in how it affects my horse? Many thanks COTHers 
The horse should be between your leg and your hand. If you are crooked, you cause the horse to become crooked. If your hands are too far apart, you create too much space for the horse to not travel straight; it also puts you in a bad position, because, for example, how do you open a rein to turn, if your hands are already “open”. If your hands are uneven, you cause the horse to tilt his head/neck, and there’s a good chance your shoulders (and elbows) are also uneven, putting you and your horse off balance. If you cross your reins, you are sending the horse conflicting aids (instead of pushing the horse around the inside leg to a balancing outside rein, you’re using the inside rein both to turn and hold him out, which is confusing for the horse) and not engaging him from behind.
Also, remember that dropping your hands does not make the horse drop his head; that only breaks the connection to his mouth. If you’re dropping your hands over a jump, I think there’s a good chance this isn’t a real automatic release, but that your hands are not releasing at all and are down by the withers, with your shoulders in front of your hands – that puts you and your horse off balance and catches him in the mouth in the air. Essentially, trying to ride a horse using your hands/reins instead of your leg makes you less or non-functional; you need to balance yourself, without balancing off the horse’s mouth, so you can balance your horse. A lot of this is muscle memory, so you have to retrain yourself to recognize what correct positioning of your hands feel like.