There is a 9 month gap in your chronology. The Susan Blake Mercer Island event was August 1961 before she had learned to change diapers (less than four days after Barack Jr. was born). She started school for Spring Quarter in April, 1962; having been in Hawaii sometime within a week after Susan Blake.
U of W is not a semester school so the usual term time table does not apply there.
Actually there is no proof she was in Hawaii after the birth, anymore than there is any sighting of her being in Hawaii before the birth! She simply “fell off the face of the earth” until the sighting of her on Mercer Island after the birth! Her mother could have been the one who registered the birth after receiving a phone call or telegram with the particulars! There is nothing to say that Ann herself registered the birth!