The lyrics of "Day Tripper" aren't super clear, but it seems to be about a relationship that the speaker/singer isn't going to continue, as the girl is flighty. One repeated section starts with "She was a day tripper." The third repetition includes the "Sunday driver" phrase:
She was a day tripperOn the other hand, the speaker/singer of "Two of Us" seems to mention only himself and his companion (each verse and chorus contains either "Two of us," "You and me," or "You and I") and their impending domestic return ("We're on our way home"). "Sunday driving" occurs in the first verse:
Sunday driver, yeah
It took me so long
To find out
And I found out
Two of us riding nowhere"Day Tripper" is all about how there isn't a relationship, and "Two of Us" is about how there is. Both contain "Sunday driving," but I think it's more significant that the girl in "Day Tripper" goes alone where the couple in "Two of Us" is together.
Spending someone’s hard-earned pay
You and me Sunday driving
Not arriving
On our way back home
We’re on our way home
We’re on our way home
We’re goin’ home
Apparently, "Day Tripper" is mostly a John Lennon song, and "Two of Us" was written entirely by Paul McCartney, but I don't know how/if that affects that common phrase.