"after dining" is correct and can be used in written English.
It is normally used to refer to the activity of having eaten dinner. For example, "We enjoyed a leisurely stroll around the park after dining."
After dining well, retired to stateroom.
Over the years, hundreds of people have died after dining on the chewy white meat.
The current menu leaves no fear of having a chilblain attack after dining here.
Mr. Carter had become friendly with Mr. Klein after dining at the hotel.
He doesn't leave tips after dining in restaurants that he will never visit again.
After dining on grapes, they leave behind signs that make vineyard owners grimace: dustings of guano.
Virginia Woolf, after dining with him, noted that he "talks incessantly" and would one day turn into a "prodigious bore".
After dining with Trump at the White House, they announced that they'd reached a preliminary deal with the President.
After dining on freshly caught sardines, I took a taxi to Paradise Beach a few miles out of town.
An 18-year-old Army private, he had complained of feeling ill after dining at an enlisted men's club.
The man known in Italy as il Cavaliere, the Knight, announced his decision not to run in next year's election after dining with Mr. Monti on Tuesday night.
