What I would do:

Get the card holder to go on ahead to the lounge, whilst you and kid wait downstairs.

Card Holder: "I know I can really only bring in one guest, but my wife and child are travelling with me today, and I wondered if there is space in the lounge if they could enter with me?"

A couple of responses may be forthcoming:

Lounge Dragon possible response #1: "Well, I am sorry, but we're really full today, so I can't make an exception to the rules"

Lounge Dragon possible response #2: "Good God, how very dare you. I will now confiscate and cut up your card and your wife"

Lounge Dragon possible response #3: "Computer says No"

Lounge Dragon possible response #4: "Well, I think we can manage that on this occasion sir. Bring them up."

By leaving the family downstairs whilst you ask politely removes most of the pressure from the lounge agent. Don't argue your case if they say no - it's just embarrassing for all concerned! Just thank them for considering, and head off to plane food or elsewhere.