In short
Joseph is not mentioned when the Magi visited Mary and Jesus because while it makes sense that a new mother would be with her infant child, there was no need for Joseph to stay at home.
When they entered the house where the star led them, the Magi saw the child with Mary his mother
(Matthew 2:11). Joseph is not mentioned, and all attention is on the newborn king. Given that this episode takes place not long after the birth, it is not strange that it is the mother that is in the immediate presence of the child.1
11 And going into the house they saw the child with Mary his mother, and they fell down and worshiped him. Then, opening their treasures, they offered him gifts, gold and frankincense and myrrh.