Actually, all the sacraments/mysteries can be taken at any Catholic Church. Even a Latin child, baptized in a Byzantine church, remains a Latin.
And, just to clarify, we now use the term "Church" or "church sui iuris in reference to the different Churches that make up the Catholic Church. The term "rite" is simply not meaningful in this case.
Fr. Deacon Edward
Thank you for clarifying terminology for me. Oy! All the things I need to learn.

So if we start attending Saint George's on a regular basis, we could in fact have our daughter (due in March) baptized there? That's great. Perhaps it would be a good idea for us to write down all our questions and speak with the priest.
Thank you!
Andrea