As already mentioned, "screaming" modifies "parents." The sentence is odd because, without context, it describes an odd situation: the parents seem unusually infantile. Furthermore, the sentence without context seems incomplete: the parents came out of what. Finally, the syntax is infrequent. It is not usual in English for adjectives or adjectival phrases modifying the subject to be separated from the subject by a verb (unless the verb is a descriptive verb like some form of "be," "become," or "feel"). Indeed the most frequent position for an adjective is preceding the noun it modifies (again ignoring descriptive verbs).
"The barefoot, screaming parents came out" and "The parents, barefoot and screaming, came out" and "The parents came out barefoot and screaming" all mean the same thing.
Adjectival phrases, however, almost always follow the noun modified. "The ready to eat ice cream parents came out" is simply not idiomatic. "The parents, ready to eat ice cream, came out" is idiomatic (ignoring the absence of any mention of whence they emerged). The post-positioning of the adjectival phrase tends to drag adjectives modifying the same noun into a a similar position so that all the modifiers are in the same place.
To sum up.
Adjectives or adjectival phrases modifying the subject may follow the verb, e.g., "The parents were happy and ready to eat ice cream."
Long adjectival phrases almost always follow the noun being modified, e.g., "The parents, eager to eat butter pecan ice cream with hot fudge sauce, drove to the confectionary shop."
Although not required, it is frequent to place an adjective modifying a noun in the same position as an adjectival phrase modifying the same noun. This is even more frequent if there are more than one adjective modifying a noun also modified by an adjectival phrase.