I cannot offer a canons-based reply, and certainly your priest will know best and you should follow his direction, but I am in a similar situation whenever I visit family, so this has come up often for me, as well. I have only heterodox (and worse) family members, so my priest has told me that when they are praying, rather than joining in verbally or becoming any kind of obstacle, I am to pray silently my own prayers, knowing that any uncertainty or nervousness associated with 'praying with heretics' can be dealt with also through the prayer. He did not say it in so many words, but I think the principle is that there's nothing that the prayer of the heterodox could do that the prayer of the Orthodox Christian cannot; if their prayer to whatever it is they believe in is anything at all (and its not my place to say so, one way or another), then certainly the prayer of a baptized, practicing Orthodox Christian is much more powerful.
In a place with many false gods and false christs, we should be more
willing and eager to pray, not less. It is too easy to remain in our little Orthodox bubble in our parishes, on the internet, etc., but what about our own biological families? Don't we pray for their salvation, too? I have to say that for myself, even though my conversion has been the source of a lot of conflict with my family (particularly given my father's own conversion to an anti-Trinitarian cult around the same time; yeah, holidays are super-fun!), it has also imbued a lot of meaning into many passages in scripture and even very basic actions that was not there before. I make the sign of the cross before eating at the family table, or I do a metania while in private prayer in the guest room of my father's house, and I am doing what I can to reclaim a little bit of family life for the worship of the One God. Who better, and in what better environment, right? These kinds of situations are exactly where God has put us, and previous people who had it much, much worse than we did in this regard actually became the catalysts for the conversion of non-Christian family members (see: Mar Behnam
), so next to them...well, a prayer among heterodox family and friends is probably the least
we can do. And yet we've got to do it.
Don't be shy.