8 yr old daughter eczema case

I began reading the eczema posts and have learned that I SHOULD stop allowing her to eat so much bread and processed foods, switch her to mostly organic foods.
Give her a banana every day.
Lots of water, no dairy.

Now here is her case:

Eczema began at 6.5-7yrs old, she was breastfed for one year as a baby--no formula. Never has had any vaccines at all. She is a very picky eater, and anytime she has tried a new food or something she did not like she would gag profusely sometimes causing herself to vomit (when a toddler-about 4yrs. old)...her favorite food as a toddler was olives (usually black olives but she liked green ones too)...she still will gag but not vomit. I have a hard time getting her to eat more healthy, but here is a list of things that she eats--most of it unhealthy stuff that I am gradually eliminating:
cheese pizza is her favorite
burgers & fries
Chicken tenders, chicken cooked in any way...
Steak
Fish sticks (minced pollock only)
Macaroni & Cheese
Bread, Bagels & toast
she has always preferred bread products
Broccoli -- raw or cooked
Spinach -- raw
Carrots --raw or cooked
Cauliflower --raw or cooked
Mushrooms -- raw or cooked
Olives (black or green)
Fresh Peas
Watermelon
Apples (but not the peel)
Bananas
Grapes

She does not like juice or tea but loves sodas (which I limit to about 1 every few weeks or so, if that)...she loves ice water to drink more than anything so I encourage that and she drinks at least 32 ounces of water each day, usually more though.

She loves milk and cheese, but I limit that now as I believe it is the trigger for her eczema.

I know her diet needs work and we are getting there (even with all the gagging)...she is very dramatic, often loud and boisterous, giddy and laughs a lot. She is not at all shy, very outgoing personality and loves to be the center of attention. A note also is that the eczema actually began after her sister was born about two years ago. She is very emotional and sensitive and will cry easily. She is very pale complexion, sunburns easily, dark brown hair, light bright blue eyes with swirls like the ocean. I believe the weight gain is my fault due to having two babies (her sister and brother) in such close proximity (17mos apart) that we were just not as active as we were prior to this, and I did not pay close enough attention to her diet as I did before, taking the easy way out in our meals.

She is short stature --a little over 4ft, in the 25th percentile, and getting a little pudgy weighing 66-68 lbs. 80th percentile. I enrolled her in gymnastics a couple of weeks ago and now work out with her every morning for 30mins-1 hr. Hoping to sweat out some toxins. Oh, and she began to have noticable body odor about 7-8months ago, I talked to the DR. about it and she said that this has been starting earlier in children--but it worries me, so I limited her milk & fried foods and it has improved.

Her rash appears on the inside of her elbows, it started out very small and has gradually gotten much larger, it is red, itchy and appears to have small bumps but does not ooze at all. Only one arm was affected at first, now both arms are affected and sometimes the bends of her knees also flare up. I applied some tea tree oil diluted with olive oil to her arms and it has significantly improved--but also I have been changing her diet at the same time. She does take a multi-vitamin supplement that is kosher/vegetarian.

Any whole foods that cleanse the body?? or other advice??

Thank you in advance for any advice,
Steph.