I think we all get our information from newspapers, internet, magazines, etc. unless we personally know Prince William and Kate. Unfortunately, even the ones you are quoting can be stated as alleged if you didn't get the information from Prince William and Kate herself and rather from newspapers, magazines, etc.
So, where did your information come from?
Can you please state your sources? By the way, since there were dating when both were over the age of 18 yrs old, then they were adults whenever they broke up and reconcile and not "kids".