Take a look at the sucess of the Eastern Rite Churches which are under the leadership of Rome, what a united Church could truly be.
The history of the Eastern Rite (Roman Catholic, called Byzantine Catholic) churches begin with two forced unions, one in Brest, Poland in 1596 and another in Uzhgorod (now Slovakia) in 1646. The people were Orthodox people who were forcibly annexed by Rome. After a number of decades, the Roman theology took root. But when many of these people immigrated to America in the late 19th and early 20th centuries, the Vatican decided to forbid married priests, which violated the terms of both agreements. Interestingly, this was only declared for America; in Poland and Slovakia, the Vatican still allows married men to be ordained. Around the turn of the 20th century, a Byzantine rite Catholic priest by the name of Alexis Toth was rejected by the local catholic Bishop John Ireland because Toth was married and had kids. Toth realized that his people were originally Orthodox and led a movement to bring them back to Orthodoxy. The great majority (over 95%) of Russian Orthodox faithful in America in 1910 were immigrants who came to America as Catholics. While some remained Byzantine Catholic, in the late 1920s the Vatican decided to frimly enforce its ban of married clergy in America, and the majority of those who had remained Catholic in Toth’s time were led by Orestes Chornock in another mass return to Orthodoxy.
The Eastern rite churches are anything but a model of church unity, and the original union of these people with the Roman church was both forced and deceptive.