A father plans to let his two conjoined daughters die rather than approve an operation that would probably save one of them.

This is a real-life variant of the trolley problem, with a crucial difference: in this case there was time to study the issue carefully and establish with near certainty what each choice would lead to before making the decision. He cannot rationally deny that his choice of "do nothing" means death for both of daughters.

His choice is a form of moral cowardice. The kind of cowardice that makes someone lose a tooth rather than get a filling. The kind of cowardice that makes someone die of late-stage cancer rather than get early treatment and survive. So even though I empathize with his distress at the need to choose between horrible and doubly horrible, I can't excuse his decision. The daughters deserve life. If you can't save both, at least save one.

I don't think that we should be more concerned about the couple because they have four other children. Having so many is a bad thing to do, but it has no effect on the issue of saving these daughters.