I would not want a high grain content, but I am not intent on avoiding all grains either. All grains are not created equally either. For instance brown rice is better than something like corn gluten, barley, or millet. There isan ongoing debate as to whether dogs are really true carnivores like the cat or in reality omnivores (requiring both plant and animal food sources). Here is one of the omnivore sides:
Dog Food Secrets: Your Dog The Omnivore There are probably more articles online trying to support the carnivore side of the debate -- but most are written by the makers of grain-free foods or the dog owners that are strict meat feeders. I'm more inclined to think they are omnivores, both due to the combination of teeth type and the fact that every dog will graze on grass at one time or another. I have one that loves new spring grass.
Wellness is a good quality dog food. Unless your dog has an actual allergy to one of the ingredients, I would not think the food is responsible for the itchiness. If anything, I might change out the Peanut Butter snack bone. Could be something in her new environment, outside or inside, even something like the shampoo you are using. I find that rinsing has to be almost excessive to ensure no itching.
As to the weight issue, she may be gaining as she turns some of the chubbiness to muscle with the new exercise and premium diet. If you think she is getting truly overweight on the food you have listed, might want to get a metabolic panel run on her and make sure there is not something like hypothyroid going on.
These are just my opinions. Think you should probably run the questions by your vet next visit for reassurance. Especially would want to make sure the itchiness is resolved. That can lead to skin problems.