DH is stubborn as all hell. Sometimes you need to blow up at them and lay it all out, and I'd say this is one of those times.
Point out that GPs are human and see every possible manifestation of any problem known to humanity and none of them - NONE of them - can be experts in all areas, which is why we have specialisms. The GP is a primary care triage service and they can and do fuck up because, again, with the human part.
Point out that when you have very young kids you no longer have the luxury of being stubborn or contrary or dogmatic, because what you want matters not a jot compared to what they need, and what they need is a father who safeguards against the possibility that he has a cancerous tumour in his nasal cavity that he's ostriching about. You do not get to ostrich in this situation. You have to face up to it and hope for the very best. That's just the breaks when you choose to have kids.
I'm afraid I think you need to be blunt as hell about the fact that his refusal to be more proactive is failing his children.
I think he's ignoring doing more because he's scared and wants the GP to be right. That's human, but it's also not good enough.
I do understand, incidentally. I've just finished rads and chemo myself, and am moving on to more drugs and surgery, no immediate end in sight. But if I'd ostriched things could look very, very much worse, and that was never going to happen because we have small kids and they come first. He needs to develop the same mindset: advocating for them means advocating for himself at this point in their lives.