Why do my daughter's cheeks turn red periodically?

The good news is that, as you mention, your daughter's skin condition does not seem to bother her very much. In other words, it is unlikely to be something serious, however there are several possibilities. One would be eczema, which is an inflammation of the skin caused usually by dryness or irritation. This can occur even when the skin does not appear very inflamed to you, and in children this age it is very common on the cheeks. Using a good skin moisturizer or an over the counter steroid cream for a few days may help. Another possibility would be a periodic viral infection. It is very common for children to get something called a "viral exanthem" when they get a cold or other common virus. This just means that they develop a red rash, which can often occur on the cheeks, and which does not require any treatment as it goes away when the virus goes away. The final possibility would be a contact irritation from food, as you mention. Some people are sensitive to certain foods, especially acids (ketchup). Some foods, particularly citrus juices, can cause photosensitivity, or redness when exposed to sunlight. If you are still worried, talk to your pediatrician!