I might be in short opinion here; but her issues your concerned with aren’t related to why you wouldn’t trust a father and child in the bath together?
You explained they have a history of being abusive, emotionally and what not. But being abusive to an adult partner does not make them an automatic peadophile? Abuse is wrong, no matter who it happens to. But you cant say “oh he abuses his wife so it’s wrong he baths with their kids” that just doesn’t make sense?
id be more concerned that there is a history of abuse, why are you not more worried for his wife rather than the kids.. since you know he’s an abuser and she’s likely in danger?
You’re also spouting about how men are more likely to commit sexual assault - this being true of course - but 59% of child SA’s are committed by acquaintances, 34% by a family member, and that 34% isn’t specific to fathers, it’s family members a overall. And 7% by strangers.
if you have any cause of concern for the safety of those children, why don’t you spend less time drip feeding onto this MN thread and report him, have him investigated and maybe try, even just a little bit to act like you care more about the kids than you do causing the drama online.
I’ll never understand how anyone can be genuinely concerned about the safety of a child and spend however long debating it online before acting on it.