As it turned out, the fourth-generation actress ended up following the family tradition, but her desire to take the road less travelled has sometimes led to problems in her career.
When she took on the role of Tilly Mitchell in Sky Atlantic’s Escape at Dannemora, Arquette tells Sky News that eyebrows were raised in Hollywood.
“A lot of business people said to me before I did it, ‘No, no, no, you can’t gain weight. No, you can’t look like that.'”
The role was that of a middle-aged prison officer, confident in her sexuality without fitting into the Hollywood concept of a “sexy woman”.
Arquette ignored their advice and the role went on to win her critical acclaim, as well as a Golden Globe, a Critics Choice award and a Screen Actors Guild gong.
It’s a formula Arquette looks set to repeat in her latest role, playing overprotective mother Dee Dee Blanchard in true crime drama The Act – based on the descriptively titled Buzzfeed article “Dee Dee Wanted Her Daughter To Be Sick, Gypsy Wanted Her Mom To Be Murdered”.
This time it was her children trying to persuade her not to take the role.
Arquette admits: “I’d never had heard this specific story but my kids had heard of it. And so I said ‘Hey you guys, I’ve got offered this thing. I might play this lady with Munchausen by proxy’.
“They said: ‘Oh no, don’t play that lady. We know that story. Don’t play that lady.'”
True to form, Arquette went her own way and accepted.
The eight-part TV drama tells the stranger-than-fiction story of Gypsy Blanchard, a girl trying to escape the toxic relationship she has with her mother.
The teenager appears to suffer from multiple illnesses and has to be cared for around the clock by her attentive mother, but all is not as it seems.
As Arquette puts it, it’s “a lie that spirals out of control”.
Minor celebrities in their own right, thanks to TV appearances on local news after being gifted a home in a Missouri, the pair quickly switch from being heroes to villains in the public eye.
While Gypsy’s supposed disabilities are very visible, it seems her mother Dee Dee’s own undiagnosed illness – Munchausen by proxy – remains under the radar with devastating results.
The mental health syndrome, which leads a caregiver to make up or cause an illness or injury in someone under their care, has always fascinated Arquette.
“It’s the opposite of every maternal instinct I can imagine.
“As a mom I think most moms would die for their kids. They would do anything, they can’t stand when their kids have pain and would protect them from anything dangerous.
“For a mother to put her child in a position that’s actually putting them in danger and that is physically harming them and that is having lasting impact is such a nightmare.”
The fear of empty nest syndrome is one Arquette can relate to, albeit on a much smaller scale.
“My daughter was going away to school and I was like, ‘Oh my God, I’m really going to miss you. I love you so much it’s so hard’.
“You know, everything is like that for Dee Dee. Times a million. The idea of Gypsy being out of her sight is like a kid going away to college.”
The innate challenges of the role excited rather than intimidated Arquette, and she has received positive reviews for her portrayal.
So, does her actor vanity kick in when she accepts such an unglamorous part? Absolutely not.
“My job as an actor is to explore different human beings, and how do you do that with your hand tied behind your back all the time and one leg in a high heel?
“You have to be free at some point, and I feel like I’ve already won an Oscar, so when do I get to just be an actor? When can I just be able to act?”
Did she ever expect to win the awards she has?
“I was like all little girls in the bathtub. You know, when you’re six or seven, holding up your shampoo bottle and saying, ‘Thank you very much’.”
And what about the Oscar, which she won for Boyhood in 2015?
“I know it happened and I remember it, and I’ve had a lot of conversations about it and I’ve seen pictures of it happening, but it also is very surreal and weird that it actually happened and feels dreamlike and strange.”
Her choice to slip into showbiz rather than a habit and sandals has paid off, and Arquette is the first to agree.
“I’ve had a very satisfying life and a rich life. The public know a certain part of me, but there’s all these different parts.
“I’ve kind of lived 1,000 lives.”
:: The Act, which also stars Joey King and Chloe Sevigny, is available on TV channel Starzplay from today.