Okay...I am wondering if your trainer is clear on all of the elements of collection? I am not the best to explain it...I can feel it, see it, and slightly describe it, but there are others on here who might be able to give you a very clear explanation.
One of the things that I have learned is that when starting out in working toward collection...getting the head on vertical is NOT the major focus.
You really have to get the horse moving with steady/balanced impulsion (impulsion being basically focused and controlled drive, not just all out speed). Your horse should be driving from behind, his back should be slightly rounded, he should feel light and very maneuverable on the forehand, you should feel like you are riding just ever so slightly uphill.
Your horse does have to learn to be soft and supple on the bit to achieve this. One way to get his body into a collected frame is to (once he is soft on the bit) keep a light contact, or ride doing half halts, and while doing so use your legs and seat to drive his body forward. Imagine that you have faced him into a wall and then someone takes his bum and pushes the back legs/hips forward into a powerful position while shortening the overall length of the horse just a bit (varies depending on what you are doing). This would cause his back to round, and his front to become lighter. The front feet being lighter will help him be able to more quickly and accurately perform various maneuvers. Depending on your horse, your legs may have to work very hard to achieve the drive needed to create this... my horse has very low natural impulsion, so I am constantly driving with my seat and legs when I want performance with effort. :)
When you have the body, you can then worry about finishing off the head. That is not to say that your horse should not take a steady soft contact willingly. You need him to accept your contact in order to drive his back end into it. Otherwise you will have a horse with a bent head whose body is sort of just running through the bit when drive is added. In the pictures, that is more of what appears to be going on.
Sorry to sound like a broken record, but the serpentines video exercise I posted is great for softening to bit and for the horse learning balance, rhythm, and self carriage. When you put all of those together, you basically have a horse that is collected. http://www.horseforum.com/viewtopic.php?t=7552
I learned it for the purposes of reining, but the premise behind it will carry over to any discipline. It is a John/Josh Lyons method that was taught to me, that I am just a big fan of.
Other good activities for working on collection are half halts, spirals, and circles (done correctly). Also, I think that hills and low jumps can be helpful because they strengthen the hind and give the horse and rider the feel for the horse working off the hind. :)
Keep working at him - he will be fabulous at it in no time. :) I knew of and wanted to achieve collection for a long time, but really could not put my finger on what it was until I was all of a sudden working my horse collected, when all of the pieces just sort of fit together. When I am not really working at it, my horse feels like his front feet are full of bricks during his stops, turns, and gaits. When I get everything working together though, it feels great. :)
I hope my novel was helpful in some way for you.