OP,
Name changed for this. However I am in a similar situation to you. I have MS. Allegedly RRMS but its behaving more like PPMS. I'm also a wheelchair user and I'm hoisted for some transfers when I am unable to transfer safely using other means.
I've also got 2 children, one of whom is 12. I claim PIP and PIP are well aware of my children. As are social services. At home I expect the children to do the jobs I cant like picking things up off the floor, carrying washing baskets, loading the washing machine, putting their own washibg away, the older one helping me chop veg for tea e.t.c. Basically the stuff you would expect any child to be doing. While my older one can cook they choose not to unless its noodles and some kind of beige thing. The younger one can fix a snack and make some toast. Neither do any family cooking.
DH have our lines in the sand. They dont touch medication, cleaning the house (unless its their own rooms as they have to keep these clean themselves), or do any kind of personal care for me. The younger one will occasionally give me a shoulder rub but this is something they choose to do and get paid for it. We have other jobs on a tariff. Basically if they want pocket money they can do a job and earn it. Very occasionally the 12 year old will hoist me but this is only ever done with the direct supervision of dh and even then all they do is press the buttons on the handset.
Neither of them are registered young carers. To be honest there's very little on offer in my locality for young carers anyway and besides the older one is adamant they dont want to be anything different to their friends. They do know somethings up though- the wheelchair and the other equipment we have in the house is a bit of a giveaway. I've always been honest when they've asked questions but I've never done a sit down and reveal type of thing.
However the reason PIP may have flagged it is because there are young carers out there doing direct care for their parents and perhaps doing things they shouldn't really be doing. I wouldn't worry in your case as you can explain exactly what they do and dont do