Are possessives determiners(his, my, her...) preferred to the definite article ('the')

1. The first sentence is the correct one when the parents in question are the children's parents; the second one wouldn't be used at all.
2. Cases of "hit me on my head" are rare, people write almost exclusively "hit me on the head".

Here is a fairly comprehensive account by a certain Rachel, Moderator at GrammarExchange, in answer to this question: "- Uncle patted me on [the, my] shoulder. As to this sentence, some people say that the definite article is correct, some say that the possessive is correct, and some say that both are correct. Would you please tell me which opinion I should follow? If both are correct, which is preferred?".

In English, it's more frequent to use possessives when talking about the parts of someone's body.
We would say:

"¢ The football player broke his arm while making the play. "¢ Put your ankle right here so we can take an x-ray. "¢ You're so beautiful! Your smile, your eyes, your teeth your hair – are in a class beyond compare!

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However, in a slightly different grammatical construction, "the" is often used in prepositional phrases related to the object of a clause (or the subject of a passive clause) when talking about parts of the body.

"¢ Look me in the eye!

"¢ Craig was hit on the head by a falling plant. Fortunately, he escaped injury.

"¢ Apply the ointment to the skin and bandage lightly.

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Sometimes "the" is used in prepositional phrases after "be" + an adjective:

"¢ That store has clothes for men who are broad in the shoulders and narrow in the hips.

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When speaking generally, or medically, you see and hear more instances of "the" with parts of the body than you do when speaking to somebody or of another person:

"¢ Then the fever spikes, often as high as 104 or 105 F, at the same time a red blotchy rash surfaces on the face, along the hairline and behind the ears. (Description of measles from mayoclinic.org)

"¢ Other researchers, including Dr. Oberdörster's father, Günter Oberdörster, a professor of environmental medicine at the University of Rochester, have shown that such particles can enter the brain. (from an article on nanotechnology in today's New York Times)

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In your sentence, "Uncle patted me on the shoulder" would be correct because of the prepositional phrase "on the shoulder." However, in an intimate, friendly conversation as this one might be, "Uncle patted me on my shoulder and told me to go to bed early" would also be correct.