what you think will happen
Yeah, that's magical thinking bullshit. Your DH/his parents didn't think him into PsA, did he? Because that would make it his/their fault for not thinking positively enough when he was a child, which is clearly bollocks. He no more thought himself into immune system dysfunction that a person with cancer can think themselves into remission or a parent of a child with Down's Syndrome can think them into not having a trisomy.
If, worst case scenario, either of your DC do turn out at some point to have something autoimmune, the treatments available now and the treatment protocols are completely different to when your DH was diagnosed - with greater success when started early. And any issues are less likely to be written off as growing pains for years before diagnosis/any damage is done. Which means their experiences will not be the same as his.
One of mine did. She got treated early and is well looked after my her Rheumatology Team because I knew the signs and could ask the right questions. One of mine didn't. But she inherited something from her apparently completely healthy father instead. Neither of DP's children have anything at all.
What I would say is that your DH might benefit from a review if what treatment he has now isn't working - I went through tons of things before hitting on the right biologic and, along with support from Podiatry, physio, exercise, occasional steroid pulses and a load of potions from the GP, I'm better now than I have been for years. DP (yep, I somehow managed to meet somebody who had Psoriasis before I had any obvious skin involvement, as I got the PsA first - he was the one who suggested I went to the GP and showed them what my skin was doing, which then led to the PsA diagnosis and the right treatment for both).
In short, it's not going to happen because you're worried about it, if it does happen, their experience is going to be different because it's another 20+ years on in developments in medical science and there's a very good chance that you're worrying about something they don't and won't have in any case.