Unless there are factors of which I am unaware, I do not see a problem with your worshiping occasionally with family who are true believers in Christ but not Calvinists by persuasion.
The Apostle Peter begins his second general letter this way: "To those who have obtained like precious faith with us by the righteousness of our God and Savior Jesus Christ" (2 Pet. 1:1). We should by this standard be able to worship with any person who has a "like precious faith."
That faith is well-summarized in the so-called "Apostles' Creed." For centuries this has been the standard for Biblical orthodoxy, and though sometimes used carelessly (such as by Roman Catholics), it helps us to ascertain whether others who call themselves Christians share the same basic beliefs that we hold dear. If your family members can readily affirm these tenets and give evidence of the new birth, there are good grounds for worshiping together.
But what of the differences between Calvinists and non-Calvinists? Do these differences interfere with worship? On occasion they do, so we need to be careful. For example, Charismatics may insert "personal revelations" into the worship experience either by tongue-speaking or by deliverances of messages called "prophecy." This makes for a very uncomfortable situation for those who believe that special revelation has ceased and that the Bible is the completed form of revelation, which is not to be added to or taken away from.
Another problem might arise over worship practices that do not follow what the Reformed churches call "the regulative principle." Simply put, this principle requires that we worship God only in the ways specified in the Bible (see Westminster Confession, Chapter XXI). In many modern evangelical churches things go on in services that are supposed to be worship but that have no Biblical warrant (such as ballet dancing, poetry reading or even a rock concert.) If you are invited to join such or similar proceedings, you might want to think twice about it.
Nevertheless, if our consciences will allow it, we ought to encourage other believers and rejoice with them. Consider these passages from Romans 14 and 15, where in the Apostle Paul urges mature believers to "receive," that is, "welcome," those of like precious faith, but whom we may think to be "weak" in faith due to past or present influences. Romans 14:1, "Receive one who is weak in the faith, but not to disputes over doubtful things". Romans 15:7, "Therefore receive one another, just as Christ also received us, to the glory of God."
We may consider Arminians or Dispensationalists to be doctrinally "weak," but they often have zeal and piety that can encourage Calvinists. If they are willing to "receive" us, let us also "receive" them that we may together worship our God and Savior Jesus Christ.
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