What Does “in Union with Rome” Mean?

A church that is “in union with Rome” is a Catholic Church. It means that the church has its own liturgies, customs, and laws but is in agreement with the Pope about all teachings of the Church. The expression “in union with Rome” usually is applied to Eastern Churches that also have branches that are not in union with the Catholic Church. There are 23 Eastern Catholic Churches that are in full communion with the Pope.

And, yes, a Catholic can fulfill his Sunday obligation by attending Mass in the Latin/Roman Church or in any of the 23 Eastern Catholic Churches (canon 1248 §1).