Especially at home with your family do you need someone from the clergy to do it?
First, we need to be with leaders whom God approves according to the qualifications of 1 Timothy 3:1-10. And Hebrews 13:17 says God expects us to obey these leaders who are mature in Jesus and who lead by example >
"nor as being lords over those entrusted to you, but being examples to the flock." (1 Peter 5:3)
And during church communion, be at home with God and with one another as our Jesus family. I offer for your consideration > 1 Corinthians chapter eleven which talks about the Lord's Supper. One thing I notice is how Paul is very concerned with how the Christians are relating with one another during the Lord's Supper. It needs to be done in remembrance of Jesus, and how Jesus has loved us is included in this remembrance, I would say. We need to have family caring and sharing like how Jesus has loved us.
So, you need to make sure you are with leaders and others who are sharing like this, with leaders whom God trusts and so He expects us to trust these leaders.
Home communion is not to be some sort of a substitute for this!! I know people can decide their church is not right; and so they are going to do some things by themselves, including what they do with their money, of course. But God expects us to find out who are His mature example leaders and obey these people, while sharing as God's family with others who share in this.
Then . . . I do think it is possible that you can at home follow the example of how communion is done in church, where you have scripturally approved leaders > 1 Timothy 3:1-10 > whom you know are of God for you to obey.
It is not Biblical, though, for us to stay in an obviously wrong church, and take this as an excuse to go do our own communion at home. We are obligated to be sharing and accountable with Biblical example leaders who are feeding us their example so we grow in Jesus and how He has us loving. And make sure how He loves is included in us as our remembrance.