I think preschool had a lot to do with it, There are so many germs getting spread around between the kids.
When my daughter started preschool (2004) she was sick ALL the time. I think it's cuz she wasn't really around that many kids all the time. She is now in her second year of preschool and she is also 4 and she has had a few colds but nothing like last school year.
I make sure she take her daily vitamin and also they make a wonderful chewable vitamin C for kids and that helps so much.
I dont think it's related to the way she eats when she is with her dad ... My daughter loves spaghetti O's and eats them a lot and actually they aren't bad for the kids a can has a whole day supply for veggies in them. Have you talked to her dad about this?