giraffes - sorry, I didn't note your name when I first posted. I hope that you have not had any trips to hospital recently.
If I were you I would think twice about training with someone who is so ignorant about asthma. Of course your trainer's job is to push you as hard as you can go, and to go that little bit further than you think you can, but that has to be done ultra carefully with someone who has asthma. It is horrible to train with someone who does not understand asthma. I joined a group once with a particularly tough instructor. Despite me telling him that I would push myself as hard as I knew I could, but sometimes I just had to drop out and catch my breath, he kept shouting at me to push harder, and not to stop. It did kind of shock him when I followed his instructions onetime, and my lungs closed up so much that with the exertion of coughing I threw up everywhere! 
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If you wheeze when you exercise, does the wheeze abate when you rest, or do you continue to wheeze? If you are not confident that it will abate within the time it takes you to return to normal breathing rate, then you will have to be very careful indeed.
Do focus carefully on your breathing whatever exercise you are doing, and try to keep it as slow and regular as possible. Make sure that every breath comes deep from the bottom of your diaphragm. I find that if I am getting wheezy, it really is not possible to breath slowly, as you just need too much force to get the air in and out of your lungs. My method for working around this, and I stress it is something that I have worked out for myself and is not medical advice, is to focus on filling and emptying my lungs as much as I can. If I can't do it slowly, then I do it quickly, but make sure that I pause and hold my breath for a second or two at the end of every inhalation. This stops my breathing getting out of control and stops me hyperventilating, which is when I really get into trouble.
If anyone reading is medically trained, and would like to tell me that this is wrong and there is a better way, I really am all ears!