Sharon Horgan is trading in her “Bad Sisters” role for one of a great mother.

The “Bad Sisters” creator and star leads limited series “Best Interests,” which centers on two parents (Horgan and Michael Sheen) who are determined to extend their daughter’s life. The four-episode limited series has been nominated for two BAFTAs, and debuts stateside on Acorn TV.

The official synopsis reads: “Andrew (Sheen) and Nicci (Horgan)’s daughter, Marnie, has a life-threatening condition. The doctors believe it is in her best interests to be allowed to die, but her loving family disagree. And so begins a fight that will take them through every stage of a legal process, as they struggle to contemplate this huge decision. It’s a story of a family driven apart by having to make choices no parent would ever want to make.”

The series begins with Marnie developing a severe infection and being placed on a ventilator,...