Two things stand out about this psalm. First, as a song of ascents it was meant to be memorized and sung by Israelite families as they pilgrimaged to Jerusalem for feast days. This explains the family perspective of this psalm, particularly its celebration of children and family in verses three through five. I envision parents singing this song with children in tow. Probably entire inter-generational extended families travelled together, singing of the blessings of family, children, and God's goodness to them.
Secondly, it was penned by Solomon. As such, it would have been a "new song" in its day. It must have been composed early in the history of the Temple then, showing us the "family-centeredness" of Israel's early Temple worship traditions. To worship God then is a family activity meant to bring all generations together before The Lord.