Angela Lansbury's Family:
Anthony Peter Shaw

Anthony Peter Shaw is the first son of Angela and Peter and was born in their home in Encino (San Fernando Valley) on January 7, 1952.

Anthony married Lee Speer Webster during a ceremony held in the Grace Cathedral chapel in San Francisco on May 30, 1980.

The couple has 3 children: the first one, Peter John Shaw, born in December 1982, the second one, Katherine, born in 1985 and the youngest one, Ian Lansbury, born in 1989.

Anthony first started a short career as an actor.

Here is his filmography as actor (taken from the IMDb):
A Bridge Too Far (1977, credited as Anthony Pullen). He was an U.S. captain.
The Spy Who Loved Me (1977, credited as Anthony Pullen). He was an USS Wayne Crewman.
Cuba (1979). He played Spencer.
The Martian Chronicles (1980, TV mini-Series). He played Edward Black.
North Sea Hijack (1980). He played Robert F. Ackerman.
He Knows You're Alone (1980). He was a Detective.
World War III (1982, TV Movie). He played Lt. Ed Spector.
The Jigsaw Man (1983). He played Matthews.

Then he became a director.
When his father Peter started his business, Corymore Productions, he worked for the company on Murder, She Wrote and other projects like Mrs. 'Arris Goes to Paris and Mrs. Pollifax. His latest project with the company and Angela was on Mrs. Santa Claus.

Here is his filmography as director (taken from the IMDb):
Murder, She Wrote (1984, TV Series. Episode "Crimson Harvest")
Mrs. 'arris Goes to Paris (1992, TV Movie)
Murder, She Wrote: South by Southwest (1997, TV Movie)
The Unexpected Mrs. Pollifax (1999, TV Movie)
Murder, She Wrote: A Story to Die For (2000, TV Movie)
Murder, She Wrote: The Last Free Man (2001, TV Movie)
Murder, She Wrote: The Celtic Riddle (2003, TV Movie)