Is 「子供を映画へ連れて行く約束した」 ungrammatical?

Question

子供を映画へ連れて行く約束をした。

I promised to take my child to a movie.

Here's my parsing:

子供を映画へ連れて行く | relative clause

約束をした | verb phrase

We need a noun in order for it to be modified by a relative clause, so we cannot use 約束する because it's a verb. Therefore, a literal translation for the above would be "I made the promise to take my child to a movie."

Answer 1

If you want to modify 約束 using a relative clause (or any other noun-modifying expressions), を is mandatory at least in formal sentences. As you said, 約束する without を is a verb, and thus cannot be modified by a noun-modifying expression.

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を is mandatory (modifiers are applied to the noun 約束):

• 大事な約束をした
• 旅行の約束をした
• 子供を映画へ連れて行く約束をした

^{(を may be dropped anyway in informal conversations.)}

を is optional (modifiers are applied to the verb phrase 約束(を)する):

• 昨日約束(を)した
• 確かに約束(を)した
• 子供を映画へ連れて行くよう約束(を)した

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See Chocolate's comment for details.