i share your frustration, especially for many hotels in Europe where beds are often single or twin. Sharing a twin bed with a child is usually very tight and not comfortable sleep and that's why it would be max occupancy 2 adults for two twin beds and 1 child likely assumes in a cot. and you usually won't get away with sneaking in an extra person (adult or kid). it's really obvious when someone is with you, even when not checking in but eventually. Many hotels have requirement to register/have documentation for all guests and that's a local police requirement, not hotel trying to be nosy so yes, they will insist on adding the person to the reservation and if it exceeds room limit, you will have a problem. It could also be a fire occupancy rule.
So, if you can't get resolution by contacting hotel directly, I would respect their occupancy/bedding rules and figure out what's the best option - even if that means a larger/more expensive room.
As a family of 4 with two kids, in the US, we easily fit into one hotel room with two double beds everywhere. In Europe, I know we'll need two rooms almost always. that's just what it is and we budget accordingly (or look for Airbnb).