@Trees5 You can refuse entry on the basis of unregistered/unapproved guests, especially the head count goes over your occupancy limits. But this level of screening isn't compatible with self-check-in. It's a lot more complicated to evict a guest once the stay is in progress than to refuse entry. And either way, you forfeit your payout.
This guest does not sound on the up-and-up - it's not normal for a parent to go to such lengths to hide their own child. I do recommend being in contact with the guest to make it known that you're aware of the child being in the home - one way to present it would be to insist that the guest accept a booking alteration to update the number of people in the booking (for insurance purposes, yadda yada). If you witness anything that raises concerns about the child's welfare, notify the appropriate authorities of course - underhanded guests should always keep you on high alert, even if the likelier explanation is something benign.
Where is the child sleeping? Well, from hosting a homestay I can tell you that I've seen just about every possible combination of two family members, all ages and genders, choosing to share a bed and seeming perfectly comfortable with it.