First of all, be warned that there are multiple terminologies for English grammar, they often use the same words to mean different things, and adherents of one terminology often feel a need to publicly denounce any deviation from their preferred terminology as the irrational, depraved gibbering of devil-spawned subhumans with severe head injuries. Secondly, be warned that often grammar has simple patterns that apply most of the time, which are pretty simple to explain, as well as complexities and variations that violate the simple patterns and are very hard to explain.
I will answer your question in terms of traditional grammar, which is far from standardized, and I will ignore the aforementioned complexities. What follows is an educated guess about what your publisher has in mind.
No, in the red shoes is not a relative clause. A relative clause is a kind of subordinate clause, introduced by a relative pronoun that refers to a noun in the superordinate clause. For example:
The man who wore red shoes came to dinner.
This is a "clause" rather than a mere "phrase" because it has a verb of its own (wore): it states something about the man. A clause has all the elements of a whole sentence inside the main sentence: it has its own subject and verb, and in this example, its own direct object. It's a "relative" clause because it's introduced by the relative pronoun who, which stands for "the man"—the subject of the main clause.
This sentence has a prepositional phrase instead of a relative clause:
The man in the red shoes came to dinner.
The prepositional phrase in the red shoes functions as a big adjective, modifying "the man". The two sentences mean almost the same thing.
This sentence has a participial phrase:
The man wearing red shoes came to dinner.
This is not a subordinate clause because it doesn't make a sentence inside a sentence. Wearing is a present participle, which is a verb playing the role of an adjective—not the role of a verb like wore in the true relative clause above.
The most common relative pronouns in English are that, who, and which. Some more are where, when, and whom.