iPhone 4 not enough memory to update with nothing on phone

My mom's iPhone 4 has nothing on the phone but a few apps. Her itunes wont let her update her software because it says there is not enough space. On her phone it says there is plenty of space but on itures it says its completely filled. What should I do to fix this problem? She tries to use the cloud which is similarly impossible to understand and there is no reason why we should be paying 19.99 for extra storage and only have a few apps on the phone for the phone to tell her she doesn't have enough memory.

I don't understand why so many people have this question and problem and there is not an answer. This phone was expensive and it should be working correctly. We should not be getting the run around just because we are using a phone that is one generation younger. Think of your typical customer, we do not have money trees. We want our iphone 4s to work past one year of ownership.