My Catholic daughter will marry an Orthodox boy in an Orthodox church in Macedonia. After this ceremony we will go to Slovakia to continue the celebration. Can we celebrate a Mass in a Catholic church (not a wedding) and repeat the promise to God to validate the wedding?
According to the Catholic Church, your daughter's marriage to a non-Catholic, without her bishop's permission, is invalid; so she would absolutely need to marry in the Catholic Church.
From the section "Mixed Marriages" of the Code of Canon Law:
Can. 1124 Without express permission of the competent authority, a marriage is prohibited between two baptized persons of whom one is baptized in the Catholic Church or received into it after baptism and has not defected from it by a formal act and the other of whom is enrolled in a Church or ecclesial community not in full communion with the Catholic Church.
The Catholic Church considers any Eastern Orthodox "not in full communion with the Catholic Church;" they are schismatics.
Your daughter can get permission to marry a non-Catholic from her Catholic bishop. Your daughter would have to
[Can. 1125 §1] …declare that…she is prepared to remove dangers of defecting from the faith and is to make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church.
And her fiancé
[§2] …is to be informed at an appropriate time about the promises which the Catholic party [your daughter] is to make, in such a way that it is certain that he…is truly aware of the promise and obligation of the Catholic party [your daughter].
Both your daughter and her fiancé
[§3] …are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.
This is going to be tricky. The Orthodox Church's rules on mixed marriages are similar to those of the Roman Church. If a Catholic is marrying an Orthodox Christian in the Church she will be required to agree that the children will be raised Orthodox. This is a major reason why religiously mixed marriages are discouraged, especially if/when both parties have strong beliefs. major
If an Orthodox spouse were to agree to a marriage ceremony in a Roman Catholic church (either before or after an Orthodox wedding), the Orthodox spouse would place themselves outside the Communion of the Orthodox Church - i.e. they would (knowingly or unknowingly) excommunicate themselves. If this was done knowingly, it would likely take a long time and sincere and active repentance for the Orthodox spouse to be received back into the Orthodox Church: they have effectively apostatized to Roman Catholicism.
I will say if you want to know more here it is from a catholic perspective:
Now I will say that in the eastern rite (Byzantines such a Maronites, Catholics, ukrainian greek catholic greek catholic, Russian Catholics, Ruthuanian catholics, armenian catholics, Melkite Catholics, Syriac Catholics, etc.) only a priest can marry a couple, Just like the orthodox. Traditionally in the traditional latin mass only a priest perform the mass of the marriage ceremony to marry a couple (which is the mass I attend to). Not the deacon.
But this website clarifies for many the question it is directly from the bishops in the United States.
For more questions Pkease ask your Catholic or if you are Orthodox your Orthodox Priest for further clarification.