The following sentence is ambiguous. Provide two explanations which illustrate the different meaning of the sentence: Visiting relatives can be problematic.

The sentence is unclear because one is unsure if the speaker is talking about the act of visiting relatives being problematic or if relatives who are visiting can be problematic. Let's break each possibility down grammatically.
The first possibility focuses on the act of visiting relatives. "Visiting" in this case is a gerund referring to an action -- the thing that is being done. "Relatives" are the direct object here, or the group being visited. The modal phrase "can be" is epistemic -- that is, it will lead us to the adjective that will tell us more about what it is like to visit relatives. In this case, the adjective is "problematic."
The only thing that is consistent between the two possibilities is the negative connotation of "problematic." Now, let's consider the second grammatical possibility. The phrase "visiting relatives" could be a subject clause. "Visiting," in this case, acts as a present participle adjective, modifying "relatives." The modal phrase "can be" now takes the form of a linking verb. Linking verbs connect the subject to parts of speech, such as adjectives, that will tell us something more about the subject. In this case, "problematic" is used to describe "visiting relatives."
This sentence could be clarified by beginning instead with an infinitive clause, though that can be awkward in modern speech: "To visit relatives can be problematic." One could also begin with a more specific gerund: "Going to visit relatives can be problematic." Finally, if one wants to focus on the relatives themselves one could write, "Relatives who are visiting can be problematic." The relative clause "who are visiting" describes the relatives to whom we are referring.