Ghosty, of course it would be a denial of the OP’s Catholic faith, in every shape and form, to attend a Greek Orthodox church and receive the sacraments in place of attending a Catholic Church. The Canon you cite in no way covers their reasons for attending the local Greek Orthodox church.
Canon law doesn’t seem to agree. The text Ghosty cites exists in both the CCEO (Eastern Canon Law) and the CIC (Latin).
The Antiochian church has a unofficial but widespread acceptance of Melkites to communion.
The CCEO canon adds that the obligation is to assist frequently at a divine worship service of “any Catholic rite”… the Antiochian curch and the Melkite church share the same rite (Byzantine) and sub-rite (Syro-Byzantine), same traditions, and nearly identical liturgies. The Rite is catholic, even tho’ the parish isn’t.
Further, the Eastern Churches not in union, per the canon Bro. Ghosty cites, are permitted. It is usually to the spiritual advantage, and in line with the vatican II directives on the integrity of the Eastern Churches, as well as the writings of popes Pius X, XI, and XII, John XXIII, and John Paul II, for Eastern Catholics to do as much as possible to retain their Eastern praxis. The directory on Ecumenism notes that attending an Orthodox liturgy fulfills the Latin Obligation, even if one has access to a Catholic Church, if one has educational or familial reasons to be there. The V II documents also note that a Latin spouse is strongly encouraged to take up the ECC praxis, in order to preserve the Eastern Churches.
So, provided she’s not indifferent to the (very small, tho not always minor) differences in ecclesiology and theology, attending the liturgy to be worshiping with her husband is a commitment to unity within the family, and a natural part of Catholic marriage. (See V II post conciliar documents.) That she’s asking indicates a lack of indifference.
He’s not doing anything wrong by so doing; the Melkite church routinely allows Orthodox to be parishioners without giving up their status as Orthodox. Further, many Melkites have been advised they may attend Antiochian Orthodox parishes when no Catholic Byzantine Rite parishes are available; latin praxis is very alien to some Byzantines. Plus the calendar differences, and more.
She has compelling reason to go, and is obviously not indifferent, and it is to their mutual spiritual advantage to share liturgical prayer with her husband at least periodically. Therefore, it’s pretty clear that she meets the standard for the canon.