Knowing me, knowing you: Rebecca Peyton and Angela Peyton

Rebecca Peyton, 39, is an actress whose one-woman show, Sometimes I Laugh Like My Sister, is based on her experiences after her elder sister, Kate, a journalist and producer, was murdered in Somalia while posted there for the BBC in 2005.

We were always aware that home was Mum's domain; Dad was area sales manager for EMI so he was away a lot for work. When he died, when I was six, we were lucky in as much as our daily life continued as it had done; we had our primary carer. We lived in a small village in Suffolk, and had lots of friends.

After he died, I spent a lot of time out on my bike, hurtling around. We have always been very close, but became particularly so after Kate died. There was a noticeable change in Mum. It was only as an adult that I realised that hurtling round on my bike when I was younger was nerve-racking for her because Dad had died from being knocked off his bike.

She's a remarkable person. If there was something we wanted to do, she let us do it without letting her anxieties get in our way. She always said she didn't want to pass down her terror and fear to us and she didn't. The best way to describe how Kate's death affected the family was that we had always been a four-wheel vehicle – Mum, Kate, Charles, my older brother, and me – and suddenly there were only three wheels and we weren't designed for that. Losing somebody changes who you are and how you relate to the world and you have to get to know the new person who's left.

Mum was incredibly supportive about my doing the one-woman show, which really puts our ordeal on stage. But she was terrified that not only would I have had to deal with Kate's death but I would also get bad reviews or people would accuse me of whatever. I guess she finds it odd but I think she's proud now.

Angela Peyton, 71, worked for EMI, where she met her husband and Rebecca's father. They moved to Suffolk and had three children, Charles, Kate and Rebecca. After her husband died 33 years ago the family continued to live in Suffolk.

It is the hardest job in the world raising three children on your own and mine weren't even particularly troublesome. When your husband dies, you have no back-up, you have to make the rules and enforce them. I decided that I really had to fight for the things that matter and after that we could negotiate.

I treated them as adults from when they were quite young, I suppose. Often people comment on how we talk to one another.

I did find it hard when they all left home but I didn't sit weeping in their bedrooms like some people do. As Rebecca was the last to leave, I knew she would be worrying about me so I thought it was important not to shoulder her with that responsibility. After Kate's death, our relationship changed a lot; I think I became dependent on her for a while, possibly even a burden. We each dealt with Kate's death in our own way. One lesson I learnt after my husband died is that you never say to anybody that they ought to be doing something in particular after they lose someone. It is so individual and so personal. Rebecca and Kate were of a generation and were so close and Rebecca was bereft in a way I didn't experience, I couldn't. But losing your child is as bad as it gets.

I did worry that people would find her play unacceptable but I grew to understand why she needed to do it. And since it's been well received I've been able to relax a bit, I suppose.

'Sometimes I Laugh Like My Sister' transfers to the Finborough Theatre in Earls Court, London, from 8 January 2012. finboroughtheatre.co.uk