Perhaps the bride's parents had an objection to the marriage and the synagogue required their permission. The couple's only alternative would have been a civil marriage (or Gretna Green?), if they were both aged 18 or older.
I would also look at the D.o.B. of their first child, to see if this was a 'marriage in haste'. That may be a clue as to why the bride's parents objected.
They also may have objected because they wanted their daughter to marry someone else or didn't approve of the groom for some other reason.
There may have been a problem for them to provide sufficient evidence of her being Jewish (not having her parents' ketubah?), so the synagogue wouldn't allow them to be married there.