The rules for the First Wing are the same as the rules for the First lounge so I think you're going to struggle here with one too many guests. You'd be entitled to one guest and your infant (under 2) won't count towards that which is helpful but technically you'd be over quota by one with your wife and 3 year old. It's possible you might get away with it though.

Alternatively, if you upgrade your wife to CW you will all have access to the Galleries Club lounge. She will have access in her own right and you can guest in the 3 year old and take the toddler. Plus, you'll earn personal brownie points