Hi and welcome
@CharliePBC. You've certainly had a rough time getting here and I feel for you.
I'm T3c; so as far as I'm concerned it definitely does exist and your son and daughter need to do some refresher training! But, jesting apart, their comments do draw attention to the lack of understanding about this variant of Diabetes Mellitus (DM). There are very few of us; very broadly 90% are T2s, 10% T1s and T3cs are less than 0.1%. So very limited awareness within the medical profession.
That said NICE do recognise it and refer to it in certain DM guidance documents.
Also, although the cause of one's diabetes leads to one's classification, within the T3cs the generic cause is damage to your pancreas. But this could be from illness such as pancreatitis leading to loss of some or all pancreatic functions (and could have been under treatment for years); damage from an accident; and total removal - in my case to arrest pancreatic cancer from a tumour close to my pancreas. So T3c is very wide ranging and of course the Devil is in the Detail. In some ways I can see why someone categorised you as T3c; there isn't necessarily a better category and you certainly now seem to have some damage to your pancreas.
As
@Kaylz said earlier, T3c is in many ways treated as T1, ie (usually) T3cs are first and foremost insulin dependent. So, while it annoys me when a medical specialist who should know better writes a report about me lazily calling me T1, another Specialist pointed out that the average A&E Doctor or Nurse might pick up on the Diabetes condition, but not appreciate that I need insulin. So don't be too surprised when you encounter Specialists who don't even know about the generic categorisation of T3c, never mind understand that it's akin to T1 for treatment, with many extra challenges.
Anyway, good luck with everything. Ask any question you need information about, no question is stupid. You are probably already detecting there is a lot of detailed knowledge about aspects of DM from members with decades of experience.