Sunday is a whole other debate, but the Sabbath is on Sunday because that is when Jesus and the Disciples met according to Scripture.
Met when? What are you referring to? Where in Scripture?
The Sabbath is biblically Saturday. The calendar you use even respects that - the seventh day - the day of rest - is Saturday. The Church insitituted Sunday as a theological nod to the fact that the Resurrection is the 8th Day of Creation - the New Creation through Christ's conquest over death. This is why Sunday is the Lord's day in Christianity. The death and resurrection of Christ are remembered at the altar on Sunday.