dont vs. duquel

There are several uses of dont, but regarding its use vs duquel’s use as a relative pronoun, there is a grammatical distinction between them: you use duquel after prepositional phrases and dont after verbal phrases. That sounds like an earful, but here are some examples to help you see the difference:

Je vois le garçon à côté duquel j'étais assis pendant le diner. -- I see the boy next to whom I was sitting during dinner.
Je vois le garçon dont tu m'as parlé. -- I see the boy about whom you spoke to me.

In the first sentence you have a prepositional phrase (à côté de) which requires de. whereas in the second one you have a verb (parler de) that needs de. 

For other uses of dont, such as to denote that something is part of a group, you cannot use duquel: 

Mes parents ont deux voitures, dont une Mercedes. -- My parents have 2 cars, of which one is a Mercedes. (...including one Mercedes)

Frank, 

there are different uses of dont (and duquel). 

The usage in this exercise is of dont as a relative pronoun indicating 'possession' - whose magnificent gilded lead statue.... in English. You can't use 'duquel' in this context. 

 Dont = Whose (French Relative Pronouns)

With prepositional phrases with ' de ', dont is usually not an option ( see lesson for exception) and ' duquel ' is correct.   

Duquel/de laquelle/desquels/desquelles with prepositional phrases with "de" (French Relative Pronouns) 

With prepositional verbal expressions with de, both dont and duquel are options. Dont is more colloquial, while duquel is generally restricted in use to specific situations as you note, and considered quite formal ( archaic as described in the lesson). 

 De qui/dont/duquel = of/about whom, of/about which - with prepositional verbs with "de" (French Relative Pronouns)