I saw your other question and it lead me here. First, when do you usually binge? If it is in the evening, this is probably because she wants you to eat every 4-5 hours so that you won't skip meals and overeat later, which may make you feel too full and trigger a binge.
There has to be some give and take when you go into treatment. I dislike how high carb my meal plan is, but I have accepted that first comes my relationship with food. I can work on tweaking my plan after I have more trust in myself to eat healthily. Nutritionists/dietitians are there for you not just to help you recover physically, but emotionally as well. Work with him/her. Don't go in fighting.
I asked to sub in sweet potatoes as a starch as opposed to grains. It offers the complex carbohydrates that meet my meal plan. If you are primal, you can also ask about tweaking your plan to have dairy to count for some of your carbohydrates. I ate a sweet potato as my first "starch" that I've allowed myself today (outside of binging), and I almost cried after feeling okay with it because it was "safe". It is freeing not to have too much emotion attached to food. I am eating to live right now, and I am okay with that. I am trying to follow my plan and am thinking of it is medicine--and sticking to paleo as best as I can.
If you binge eat, the point of trying to get you to face your trigger foods is so that in the future, if someone asks you to take a bite of cake at a party, or you have just one small "lapse" that you can sit with the feeling, understand that you have control, and not turn it into a full-fledged binge. You have to learn that one bite of a "unsafe" food means that you still have control--that you don't have to give in, say, "screw today" and give up.
You talk about one bite of wheat sending you out of control. You know, after recovery, you never have to touch wheat again. But the point is to not view it as a "bad food" that you will trigger a binge anytime you eat it if you.
ED recovery is about re-wiring your brain to respond differently to environmental cues, and this includes triggers that come with certain foods. If you are at a social outing, for example, and you decide to take a bite out of bread for the first time in say, 4 months, it should be okay. Lots of people on here have slips, eat 80/20, or will occasionally eat something non-paleo. The trick is to train yourself to respond to that emotional feeling towards food...are you going to throw in the towel and binge? Or are you just going to take that bite, not see it as a "trigger food" and move on with your life?