@Aisling29 I think your intuition is right here for many reasons!
You're a live-in host with a child as well as pets in the home, so Instant Book is not a good fit for you. It's of the utmost importance that you do some judicious screening before confirming bookings. For past reviews, for confirmation that they understand the nature of your household, and to be sure that their communication leaves you feeling safe.
The only area where we disagree is that "Superhost status" is worth anything at all. It's not. It's a manipulation tool with no tangible benefit to your business, and costs people far more in anxiety than it pays back in reward. Your judgment as a host and parent should always come before any concerns about those star ratings.
Shame on @Airbnb for telling you, incorrectly, that it's "discrimination" to refuse a guest on the basis of a bad review. Discrimination as it pertains to Airbnb terms is defined here: https://www.airbnb.com/help/article/1405/ . Relevant quote: "Nothing in this policy prevents a host from turning down a guest on the basis of a characteristic that is not protected under the civil rights laws or closely associated with a protected class. "
Obviously, people who have received extremely bad reviews do not constitute a "protected class" by any stretch of the imagination. What's the point of reviewing guests if hosts can't use them to make decisions?
I'm glad you got out of this booking and encourage you to escalate a complaint about the agent who handled your call (on social media, if necessary). Threatening a single mom with penalties for not accepting a man with a documented history of aggression to other another female host is a new low, and Airbnb owes you a serious apology.