Yes, she is a distant relative, because she’s not his father’s sister, she’s his father’s HALF-sister. Keep in mind that Muslims tend to have large families (his father’s family is Muslim.) Obama has had very little contact with his father’s family, having been raised by his mother and maternal grandparents.
Actually, she was at his Senate swearing-in in 2004, not 2005. I don’t know what month it was, so I can’t vouch for the timing of whether it was before or after her residency request was denied. In any case, she attended independently; he did not “bring her.” She called him two years ago to let him know she was in Boston, but he did not see her there. That was the last contact the two of them had.