Thanks for that, do you think I’ll be able to find someone at Newcastle who can do it? Any hints I might need to give them?
My experience of Darlington ticket office (also run by VTEC) is that they're up for finding odd things (they were going to be my fallback ticket office if Redcar had refused) so hopefully that will translate across to Newcastle as well.
Choose a time of day when they're not likely to be busy (so Friday afternoon or the morning peak would be a bad idea). Be polite and friendly and explain exactly what you're after and why (they almost certainly won't have heard of a Gold Card let alone the discounts it offers). Make sure the railcard application form is completed in advance so you can hand that over at the same time. May be worthwhile having the relevant page of NRE to hand (but don't lead with "It says in NRE...").
Perhaps something like:
"Hi, I'd like to buy a 16-25 Railcard for my daughter here's the application form. I have a Gold Card which I believe entitles me to a discount off the price of any railcard?"
They will doubtless be confused and may say that they've never heard of such a thing so that would be the moment to drop in the NRE bit and gently try and hint at looking it up on their own internal system.
"Oh, but it clearly says on this page [show phone screen] that I can get a railcard for £10? Could you just double check for me? I live down South and my daughter lives up North so it would be much easier if you could issue it for me here today"
Just keep the tone polite and friendly but don't be afraid to push a little bit (i.e. don't just let them steamroller you with a blanket no). I always find playing the nice and friendly but somewhat oblivious passenger works better than quoting chapter and verse at them and risking coming off as a know it all or telling them how to do their job.
If they do refuse pointblank then I'd suggest trying again on another occasion when there are likely to be different staff working.