How easily can you change GP and pediatrician? Or if it's not pediatrician (it is for us) then child psychiatrist.
Look at the pathway - GP, then child specialist, then neuropsychologist. In your case that pathway is blocked. Why? Where? How? You have to ask - can I find an alternate pathway? If your path up the mountain is blocked by a sudden landslide, sometimes you can find a way around the immediate blockage. But sometimes you have to go back to the bottom of the mountain and start over. You could struggle for months digging with a spade, only to find as you remove the soil, that when the landslide happened, that whole area slid into the sea.
If you cannot find another specialist to refer you, then you need to find out why. If your child sees ten different GPs and none of them feel a neuropsychologist is warranted, then we have to accept that they may have sound reasons for this.
But if it's only one so far, then a second opinion, from a practice not related to the current doctors, would be worth considering. I can't advise more specifically because your health system is different to ours. We have choice here in Australia, if I don't like what my GP says I can go to a new GP and 'shop around' until I get one I feel I can rely on. If I already have knowledge of some specialists, I can ask my new GP to please write me a referral to Dr J who we saw before, when we were being cared for by a different GP. Or I can say, "I saw Dr J, I was not impressed. My friend said Dr G was marvellous for her child. Can you write me a referral for Dr G?" and unless the GP feels there is no need to see any such specialist at all, the referral generally get written.
In your case I would also have the option of 'taking a holiday" from the current GP, finding someone who will refer us to the specialists we want (including eventually the neuropsychologist) and then going back to the original GP (should I want to) with the results and saying, "Here are some answers. Will you go on with us from here?" Some doctors would show you the door - those I would happily leave, anyway. Others would swallow their pride and say, "I was wrong - I accept this. What shall we do now?"
In our case, We've done it three different ways.
First - easy child 2/difficult child 2 was seen by a public clinic at the age of 4. The assessment took several sessions and cost us nothing (government paid for it).
Next - difficult child 3 was assessed, privately. It cost a lot. it was good value.
Later there was a research project we heard about, wanting to assess kid with an autism diagnosis. We registered and got a partial neuropsychologist assessment which was very useful. Because it was research, it was free.
After that - The GP referred difficult child 3 to a therapist. The therapist we actually hears about through the oxytocin research project that difficult child 3 was involved with. They have therapy as well at the research centre. Because the therapy is separate, we needed a referral. But because we were part of the research, we were able to get appointments with the therapy unit. But here we needed to go to the GP and say, "We've got the chance to get some therapy. We need a referral from you; will you write one please?"
She did, a bit reluctantly.
Then therapist & I were talking and I said I felt it was time for another neuropsychologist appointment. therapist referred us, but it was going to cost. Not as much since it was part of a teaching unit too, but still expensive. A GP referral would not have reduced the cost. But the GP got a surprise when I said, "Here is a neuropsychologist report we had done."
So there can be other pathways, but it really depends on what else is available in your area.
Marg