Catholics are requested by the hierarchs of their own Church to respect the Orthodox stance on these matters - and the stated position of the Orthodox hierarchs in the US is, with few exceptions (chiefly on the part of the Oriental Orthodox Churches) that Catholics may not be communed in their Churches.
Among the Eastern Orthodox, there are some (but, now, few) Antiochian Orthodox parishes who will commune Melkites who are family members of their parishioners (it was once commonly accepted that this could be done). The situation differs in the Middle East, where acceptance of that practice is more widespread and informally acceptable to them.
When you receive the Mystery of the Eucharist in an Eastern Orthodox Church, you may indeed, as the lady said, give scandal to its parishioners. Additionally, you are essentially asking the presbyter to be disobedient to the mandates of his bishop - not sure you really want to be an occasion of sin to a priest - it somehow sounds like a sin to avoid.