I heard that when parents pray for their children Allah accepts it instantly. Does Husband-wife's prayer does the same thing?
I have not heard what you heard, instead there be hadith:
The Messenger of Allah (ﷺ) said, "Three supplications are answered without doubt. The supplication of the oppressed, the supplication of the traveller, and the supplication of the parent for his son."
Hadith does not say husband-wife.