Did Rome force Latin on the Eastern Churches?

A Greek Orthodox Christian's words are marked in fleches

Didn't they also want the language of their services to be served in one language (Latin), and change other things they did not like (instead of changing themselves)

In general, the Popes of Rome didn't demand that the Eastern Church replace its Apostolic liturgies or use Latin rather than Greek or Slavonic.  The Popes defended Sts. Cyril and Methodius against their local Roman enemies in Moravia who criticized them for worshipping in Slavonic rather than Latin!  However, it is true that there were certain situations (such as in Jerusalem or Antioch during the Crusades or in Constantinople itself after 1204) when local Roman bishops replaced the Byzantine Greek Liturgies with Latin Liturgies, and the Pope approved of this.  But this was because the aristocracy in those places was Roman Catholic at the time, and it was fitting that they should be able to worship according to their own tradition.  But, the Pope never authorized the wholesale replacement of the Greek or Slavonic Liturgies with a Latin Liturgy.  In fact, there were ALWAYS (and are even to this day) Byzantine Greek parishes in Rome itself, and the Pope of course fully approved and supported the dignity of the Eastern liturgical traditions.  

On the other hand, the Byzantine patriarch attacked the Latin churches in Constantinople itself  - - Latin-speaking churches which existed since the time of Constantine; and he declared that their Eucharist was invalid because the Romans use unleven (rather than leven) bread -- something that the Western Church (along with the Armenian Church) has always done since the time of the Apostles (Jesus Himself used unleven bread at the Last Supper, since it was a Passover feast and there would not have been any leven bread in Jerusalem at the time). But, the Eastern Patriarch Cerularius tried to force the Byzantine rite on the Romans living in the Eastern Empire. So, he took armed soldier into the Latin churches in Constantinople, and had them open the Tabernacles and throw the consecreated Eucharist in the streets.  This is a historical fact.  It is discussed by both Kallistos Ware and by Meyendorff in their books.  And this is why Rome (a church which continued to permit and encourage Byzantine worship in its own city) served Cerularius with a bull of excommunication in 1054. Cerularius did this because the Franks who were vassals of the Roman Empire were gaining political power in the Balkans and so the Emperor and Patriarch wanted to brand them as heretics and thus reject their authority in the Balkans.  

Charis kai eirene (Grace and Peace)

Mark Bonocore

Lord Jesus, let Your prayer of unity for Christians
become a reality, in Your way.
We have absolute confidence
that you can bring your people together,
we give you absolute permission to move.
Amen