Just flying a kite here - songs that might be amusing for a younger woman and older man to sing together.
Obvious ones like

The Old Man from over the Sea
MAIDS WHEN YOU'RE YOUNG NEVER WED AN OLD MAN

Broken relationship songs - eg

Marrowbones [see THE OLD WOMAN FROM WEXFORD]

Modern abusive relationship songs

(we are DEFINITELY going to do the Civil Wars' Poison & Wine - it's the song that started the whole train of thought)

Gaggingly twee ones - we might do "Ginny come lately". Maybe the Sinatras' "Something Stupid" (probably harder than it sounds)

What we need are some suggestions where the girl is the patsy

Young Girl
Don't stand so close to me
Go away little girl
Maybe "Wake up little Suzie"

Or nasty ones like

GOOD MORNING LITTLE SCHOOL GIRL

Over to the panel for discussion!

[Many song titles in this thread have been converted to links by a Mudelf.]