Okay this is quite interesting
The Catholic Church take no issue with us partaking in the Eucharist in an Orthodox Church yet the Orthodox Church does take issue with us doing so…
likewise
The Catholic Church welcomes Orthodox Christians to our closed communion - yet the Orthodox Church prohibits it
Yes, Catholics may receive in Churches with valid sacraments under the following circumstances:
Can. 844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, **who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of **§§2, 3, and 4 of this canon, and ⇒ can. 861, §2.
§2. Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.
And administers them to members of Churches with valid sacraments in these conditions:
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.
So if we partake in the eucharist in an Orthodox Church - do they teach we have committed a mortal sin?
(a) The Orthodox do not have the same concept of mortal and venial sin that Catholics do.
(b) The Orthodox do not have authority over Catholics, so it’s irrelevant what they teach on the matter
Likewise if an Orthodox Christian takes communion in a Catholic Church - does the Orthodox Church teach that they have committed a mortal sin?
An Orthodox who does so would be excommunicated in their own Church.
how does the Catholic Church handle this?
Handle what?