Welcome to FT!
As you rightfully guessed it is not IDB situation because you and your family didn't have valid tickets for the Eurowings flight and technically Eurowings didn't deny boarding (because you were never entitled to board their flight in the first place)
You need to take this up with LH but I would not label your complaint as IDB because neither Eurowings nor LH denied denied you boarding of a Eurowings or LH flight respectively.
It is well known that in situations like this LH call center agents have no authority to rebook you on other flights than LH group flights.