Would it also be correct to have the prepositional phrase at the end and the relative clause next to the noun?
Example A: "There were things that the child could have put in its mouth strewn on the floor."
Or would it be more logical to reverse it.
Example B: "There were things strewn on the floor that the child could have put in its mouth."
Actually, "strewn on the floor" is a participial clause, not a prepositional phrase. These clauses work better immediately after the noun, without the interference of a relative clause, as in Example (B), or at the beginning:
C: Strewn on the floor were things that the child could have put in his/her mouth.