To me, this just seems like an extremely personal matter, between you and your parents, and your parents and God. I don't think you will find a satisfactory answer on a forum.
If, in general, Orthodox people are not going to Orthodox churches, I believe they should be encouraged to go to Orthodox churches and to examine their reasons for not going, and also consult an experienced Orthodox spiritual father. (I would add, from an Orthodox perspective, given our historical experience of "sheep stealing," that it would be less "offensive" to many Orthodox if you encouraged your parents to go to a church of their faith than of yours--that is just my opinion. I have had experience living in a mixed-faith home. I don't say in your case, but in many cases what might be considered by one a "friendly invitation" carries with it a more mixed meaning. I'm sure that you only want your parents to experience the kind of spiritual meaning you have in your life, but they will need to find this on not just their own terms, but, if they are going to take their baptism seriously, on the Orthodox Church's terms, for they pledged at baptism to be faithful to her until death.)
For purposes of prayer, it is better for Orthodox to pray at home than to visit non-Orthodox churches out of convenience.