I suspect IAB deeply, deeply, U, so perhaps I want you to talk me out of this, but...
Very long back story here, which I'll try to skip as much as possible. DS (6)& his cousin (also 6) are and always have been very, very close. DP, my brother, SIL & I ran a business together, so shared childcare. 18 months ago, I had a pretty catastrophic nervous breakdown, numerous suicide attempts, was generally in a very bad place (mainly due to pressure from work, and lack of support/bullying from brother & SIL). We left work, moved away, but tried to keep up the relationship between DS & DN as much as possible.
Brother & SIL had no real contact with DP & I, but it all got very messy, with legal action against me. My sister fell out with brother and SIL, my dad no longer speaks to brother & SIL, my mum...it's complicated... Brother & SIL have now sold the business and moved ten minutes away from us.
We had, until fairly recently, still had DN to stay/play quite regularly. He stayed the night only 10 days ago. But more stuff has come out. I found out that SIL has told A LOT of people that the reason we moved was that I stole money from the business and did a runner. She's referred to my being sectioned as 'her little stunt'.
And now that my DN is so close, DS & DN are constantly badgering me to let DS go and stay at my brother's house. I DO NOT WANT DS STAYING IN THEIR HOUSE. So far, I've been very non-committal 'hmm, let me check my diary when I get home, no sorry, we're busy, can't I'm afraid.' DS isn't happy about it, and can't understand why I won't say yes, especially when my brother tells him 'of course you can stay any time you like'.
I wouldn't ever tell DS the full truth of what's gone on, but AIBU to explain that my brother & I have had a falling out, and that's why I don't want DS to stay? DS is a nosy child, so I would have to provide information of a vetted kind.