You're talking about being part of the Body of Christ of course - I believe this is what you understand to be the remnant.
A remnant is the last part of a thing that perfectly resembles the first part of that thing. The Bible says the "remnant church" will be keeping God's commandments, which means
these commandments have to be the same commandments kept by the early church.
Catholicism - by her own words - disqualifies herself as the "remnant church"
because they claim to have changed God's commandments and thus cannot trace herself back to the early church.
I believe Christians - Gentiles - had begun celebrating the Eucharist - communion - right after Jesus died. They were known as cannibals by some. I do believe they were doing this on the first day of the week, Sunday, to celebrate the resurrection of our Lord.
There's no Biblical proof of the early church celebrated what we call the "Lord's supper" on Sunday - if we choose to believe that, fine, but we can't base a doctrine on that.
If we want to understand that Peter WAS, in fact, the first Bishop of Rome, then I'd have to believe that the CC went back that far. I can't make a commitment as to how far back it goes, but I do believe it was the first church, or denomination if you will.
The reasoning for the idea Peter was the first bishop is rooted in flawed hermeneutics and extremely bad scholarship - because a comparison of the Greek words "Petros" (Peter) and "Petra" (rock) reveal that Jesus was NOT referring to Peter as the "rock" upon which He would build His church. He was referring to
Peter's confession that Jesus was "Christ, the Son of the living God" as the thing upon which He would build His church, according to the Greek.
If so, I can accept that the CC changed to Sunday IF that's how far back we want to go.
Otherwise, we have to keep to the idea that the Apostles themselves changed the celebration day from Saturday to Sunday and keep the CC out of this.
IOW,,, I'm not sure.
Actually, church historians write that it was Sabbath that was universally kept by the early church, with a few churches keeping both Sabbath and Sunday.
Proof that Sunday is absolutely not part of the New Covenant:
The New Covenant - in which the Holy Spirit writes God's Law of Ten Commandments on our hearts (2 Corinthians 3:1-3 KJV) - was ratified when Jesus shed His blood on Friday, just as the Old Covenant was ratified with the blood of bulls and goats. Everything that was to be part of the New Covenant had to have been included before it was ratified: baptism, the Lord's Supper, Holy Spirit gifts, etc.
QUESTION: When is Sunday keeping supposed to have commenced?
You see? Even if the Sunday Jesus rose was kept by Christians, it could not have been part of the New Covenant because the New Covenant had already been ratified 2 days before Sunday arrived!