There are TWO Ukrainian Orthodox Churches. I know the problem with one (from my bishop-friend who is no longer in New England and has not been for a long time; he was moved to Chicago and is not part of any of the three at all, he's OCA) has to do with a "self-ordination" at the hand of a dead bishop. A parishioner from the other one said their priest was pushing the idea of affiliation with the Autocephalous Orthodox Church of Ukraine (independent of Moscow).
And one that is affiliated with a very strict monastery in Boston (where they've always had the picture of the Czar inside the front door with an oil lamp in front of it).
None of them are OCA or Greek Archdiocese.
The Czar and his martyred family were canonized as Saints in Russia, so for his icon to be in the church with an oil lamp is nothing "unacanonical."
... pushing the idea of affiliation with the Autocephalous Orthodox Church of Ukraine (independent of Moscow)
You obviously don't know much about Orthodox Church but a good summary can be found here along with a detailed list and descriptive links for each "regular" and "irregular" church.
You know, I got to thinking about it after I sent my last message, and the most likely way I could imagine your situation there would be if you had one of those intra-Ukrainian messes plus a HOCNA parish. And that's exactly what you have! Talk about having a non-harmonic convergence... :-)
As Kosta points out, the MP has officially recognized the Royal Martyrs (although they classify them, probably more appropriately in the case of most of them, as Passion-bearers -- as with SS. Boris and Gleb -- rather than Martyrs) as saints. Many OCA parishes, including ours, have icons of the Royal Martyrs/Passion-bearers of Russia.
I would also point out that it has been the observations of many of us who travel a lot that the farther north and east one goes in America, the more the churches are tied to ethnic enclaves and the poorer the relations between parishes and jurisdictions. I know that within the ROCOR, for instance, the Eastern American diocese is notorious for the extreme tendencies of its clergy (and is where most of the opposition to reunion with the MP was centered), whereas out West, the OCA and ROCOR parishes and clergy tend to get along very nicely.
In the Seattle and SF areas, the OCA and ROCOR parishes work closely in their assistance and ministries to recent Eastern block emigres.
I've lived in 6 cities with a total of at least 18 Orthodox parishes in the nearly 2 decades that I've been attending Orthodox parishes. All have recognized the others as Orthodox, and having joint services for special occasions and during Great Lent are common. Each parish has its own "flavor," just as every individual family has its own "flavor" in an extended family.
I have never lived anywhere where there was a parish representing itself as Orthodox that was not a part of the bigger Orthodox community -- either because they believed themselves alone to be Orthodox or because the others considered them not to be Orthodox. It certainly happens, but it is not the norm of the American experience.
There have been any number of intra-ethnic "political" divisions in the "diaspora" because of Communism, but little by little they are being healed. The Serbian division was healed in recent decades, the ROCOR/MP division is nearly healed, and God willing, the Ukrainians will get things straightened out. Likewise, there are still splits within the Carpatho-Russian community.
But frankly, all of these divisions are becoming very peripheral "side-shows" on the North American Orthodox scene. A big reason for this is that virtually no converts are attracted to these jurisdictions, and even their own members and children don't want anything to do with it, frequently gravitating to healthy Greek, OCA, Serbian, ROCOR, and Antiochian parishes (and there are, of course, parishes within each of those jurisdictions that are either more, or less, healthy, as the case may be -- it varies.)
But even in the unhealthiest of situations, one is unlikely to show up at Liturgy to find things going on around and behind the altar that one encounters at our local Catholic parishes where I live. Both Catholicism and Orthodoxy in America have, in practice, plenty of warts. You obviously would rather deal with the kinds of warts that Catholicism has, I'd rather deal with the kinds of warts that Orthodoxy has to deal with. All the more reason for us all to live and let live, maintain cordial relationships, and to leave talk of any kind of union for another generation...