To follow up, at HAM they told me I could only being one guest but then said my 2 year old would be ok this time. I was 100% on board with things either way (happy to take my baby to eat lunch while my wife explored the airport and told them I'd have been happy that way) but the SEN lounge attendant went out of her way to welcome us more generously than needed.
United *g digital card, eurowings boarding pass, and no other credentials requested except my wife's boarding pass (they decided not to scan my baby's).
This will be moot soon, once we both hit 1MM and lifetime *G, but was interesting.