What is the proper word order when a sentence contains an adverb using 地 and a coverb phrase?
In Chinese you can also say "他会很诚恳地向你道歉" in this way: "他会向你很诚恳地道歉"

Then the order of coverb and adverb is the same as the sentence "父母应该把事情好好地告诉孩子."

Example: the following 2 sentences have the same meaning

coverb first, adverb after: 医生*对他*仔细地检查

adverb first, coverb after: 医生仔细地*对他*检查