When a woman gives birth vaginally, she is likely to tear. When she is sewn up, the Doctor will ask the father if he would like a few extra stitches. This will ensure a tighter vagina after giving birth.
The father was afraid that his wifes vagina would be loose after giving birth. So he asked the doctor if he would give her a "daddy stitch"
Stitches to repair rips or tears resulting from a vaginal delivery of a baby.
ie, the Doc put in a few extra daddy stitches after Jr. was born.