S.B.
As a mom of a large family, I do not expect that they ALL get invited to the same functions (even though 4 of the kids are very close to the same age). Especially as they get older, the separation of "friends" gets more and more evident as age and gender play more and more of a factor. However, I like it when the mom comes and talks to me directly first, rather than hearing it from one of the kids. Just give the mom (or dad) a call and tell them that you are doing the birthday thing a little different this year and just the 9 yr old is invited. Should be no problem whatsoever :) Since they ALL do play together sometimes, maybe the week of her birthday, when they are all outside playing, you could send out a fun treat like popsicles or something for all the kids to have in honor of the b'day girl.
Good luck!