It's such a daunting thing to face, I can entirely understand your reticence.

I'm just wondering though, perhaps bringing it up is your dad's way of coping, perhaps he needs to do this in order to come to terms with her impending loss himself? Perhaps he's not talking it over with your mum because talking about her funeral arrangements is not something she's able to do in terms of her own acceptance of the inevitability of her condition.

My dad died of cancer almost two years ago, and there were many things him and mum simply didn't discuss, presumably because they were trying to cope with things as best they could in their own way, and also trying to protect each other from more pain.

Perhaps you can explain to your dad why it's so difficult for you to talk about the funeral arrangements, but that you will try your best to help if it's what him and your mum need. At least then he knows that it's something you are struggling with, but that you are willing to do what you can to support him and your mum. But from my own experience (and I say this without knowing your family dynamics so forgive me if it's not appropriate advice) I would be cautious about suggesting that he discuss it with your mum as it may not be something she can handle.

What you and your family are going through right now is one of the most heartbreaking things anyone will ever go through, and I send you strength and love to help you through it.