The two also acted alongside each other in the 1985 theatrical revival "The Seagull" and the 2007 movie "Evening." In a 2003 interview with UK newspaper The Guardian, Richardson talked about taking on the same profession as her mother.
"I don't know if I could ever put myself in the same category as her," she said. "She is one of the greatest actresses of our time, so I'm not sure I would put myself in that bracket."
She expanded further in a 2005 interview with The Independent.
"I know the pressures of being the daughter of a great actress," Richardson told the newspaper. "But it's inspiring. You learn so much that other people don't get to learn until later on. My father being a director, I learnt a real work ethic. You think: 'One day, I'd like to be as good as that.' But when I was starting out professionally, I had a level of attention put on me that I didn't deserve or wasn't ready for. And it was hard, particularly in England, to make my way. That's partly why I moved to New York, where you can be who you are for your work and not so much to do with family baggage."
But in the same interview, Richardson talked about how she didn't want her sons going into acting.
"They'd be the sons of a great actor," she told The Independent. "And that's quite a gorilla to carry on your back. This profession is very tough and not many people make it , and even if you do, then you can still get slapped in the face constantly. So I hope they do something else -- but if they're determined, so be it."
Additional reporting contributed by ABC News' Sharyn Alfonsi, Monica Escobedo, Emily Friedman, Lindsay Goldwert and Luchina Fisher.