It wasn't his place, but we don't all react perfectly under pressure.
The OP was planning on marrying him. She's said her DD hates getting in cars with strangers (but is capable of getting a taxi as she's done this a few times) and suffers from anxiety. DD is happy for him to drive her around. He's driven her around loads, especially since her DF has been sick. All of this suggest that he's close to the girl and understands what her struggles are.
He didn't refuse to take her on the grounds he was fed up but that he didn't want to scar her for life.
It's entirely possible that based on the above and his own traumatic experience of watching a relative die, he was trying to act out of kindness, and was lashing out as no one was taking his opinion seriously, and he wanted to protect the girl.
I don't think it was his call. Given her age, I think it was DD's call. Ultimately, he took her because she insisted - not because the OP did.
But I'm not sure he should be written off as easily as some posters are suggesting.
People always say they want to be with a loved one when they die, but it's absolutely horrific to watch when they die from something they've been fighting for a while. Death doesn't always come quickly, even after The Call. It's messy and it's horrible, and it means your final memory of a loved one is them looking like a version of themselves that doesn't reflect your life with them. Witnessing the actual moment when they die is haunting.
I'm glad I was there and yet hate every part of that memory. It's complex. I can see why an adult would want to shield a child with poor mental health from that pain.
He could very well have been trying to kind. Why assume he was trying to be cruel?
As for being a grown up human - well, so am I. But I don't think I'll ever not feel scared for life. I'm crying writing this post, that's how strong those emotions still are, and I think will always be.
DD was always going to be devastated. Maybe DP was trying to make her a tiny bit less devastated but didn't handle it correctly.