Whatever the result, even if this is all innocent by someone who doesn’t know about how to interact with kids, I think it’s better to be safe than sorry
Unless you're Keith of course .
You've set the ball rolling, ably assisted by faceless posters, told BIL and SIL their baby sitter is unappropriated and emailed his previous family for opinions on his behaviour.
So if Keith is ""guilty"" (of what exactly, has a crime been identified yet?" will you go to the police? And if Keith isn't guilty how are you going to repair the damage done by heavily hinting he's a paedophile with a specific predilection for little boys?
So far, this thread has your mum married to an old perv, who you freely admit you don't like, your DB is wanting to go round and kick his head in. They clearly are not going to have any child care from your mum and Keith regardless because if I'd been called a paedo, unfounded, no amount of apologies would make me go anywhere near a kid ever again.
So whilst I sincerely hope you are wrong in your assumptions for the childs sake, what happens to Keith, if this is unfounded on your part and you've set off all these malicious allegations and rumours?
This is why I said it best dealt with by the authorities, not vigilantism. Very lucky you remembered a friend who works for the NSPCC on hand to give advice. I hope he told you not to gossip in case you are (a) wrong (b) alert the person so they can moderate their behaviour/destroy evidence..