Your immune system is your blood cells. If your cells are weak or damaged they cannot fight off an infection very well. What weakens them? Eating too much processed or cooked food. The simple act of cooking depletes 50% or more of the vital nutrients and vitamins that our blood cells need to regenerate so that they can keep us healthy and combat virus and bacteria.
So think of food in terms of regeneration. Are you feeding her high potency real food vitamins? Or is the majority of her food cooked, or comes from a box or bag? If the latter is true, then it's no surprise she is sick.
Some suggestions: get your hands on a juicer. Buy as much juiceable produce as you can. For a child, carrots and apples are usually big hits. With that base, you can mix in beets. Or try a little spinach and kale. The more green you can get into her the better. Why fresh juice? It is the fastest way to get her cells concentrated nutrients. Organic is best of course, but do what you can.
Try eliminating dairy for a while or forever. Dairy is inherently mucous and imflammation causing. Those two things in the body means longer healing time.
I am not saying that you can't eat cooked food. Especially in cold climates like NYC in the winter, cooked food is necessary to keep the body insulated and satisfied. But add in raw foods whenever possible. You can always do a partially raw soup. It's a cooked base with finely chopped raw veggies for texture. Two slices of whole grain bread on the side. Very filling and delicious.
High nutrient potency foods you should try to include whenever possible:
avocado, kale, carrots, cabbage, spinach, sweet potatoes, celery, nuts and seeds...etc.
If she's had pneumonia, she has likely been on a lot of anti-biotics. Anti-biotics are known culprits that produce or inflame candida. Candida is fungal yeast in the blood. It is a common cause of yeast infections, longer healing time, fatigue, fibromyalgia symptoms, etc. It may be worth your while to talk to a holistic health practitioner locally and see if you can get her on a short term candida cleanse. This will help her body get off the anti-biotic cycle and clean the blood.
Good luck, I feel what you are going through.