Okay, assuming the account of her travel is correct, consider this: if one were to travel abroad - even for an extended period of time - would that mean one's citizenship was forfeit?
Additionally, it would be nice to know the name of the father on the birth certificate. If it was indeed Obama Sr., he is instantly a British citizen also by birth.
Assuming that is correct, does it make a difference? Is there some provision in the Constitution or statute that declares dual citizenship holders ineligible to be POTUS? Last I knew, US law gives little attention to dual nationality. Now if you are a citizen and apply to become a citizen of a foreign country, then you risk losing your US citizenship. But that is nothing like an accident of birth that makes one a dual citizen.
Please spend some time reading the above posts about immigration and citizenship laws.