1. She kept her promise to visit her aunt regularly.

2. She kept her promise that he would visit her aunt regularly.

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Are both the same in meaning?
And is 'her' promise' in apposition with the 'that clause'?
In Sentence 1, does 'to visit...' modify 'her promise'?

3 answers

There are no appositives here. #1 is better wording than #2, but both are grammatical. "kept" is the verb. "promise" is an adverb telling what was kept. "to visit" is a prepositional (adverb) phrase modifying "promise", telling what the promise was.
See your previous post.
1. She kept her promise to visit her aunt regularly.
She - subject
kept - main verb
her - possessive pronoun, modifying "promise"
promise - direct object
[to visit her aunt regularly] - infinitive phrase that could be considered either an adjective phrase, modifying "promise," or an essential appositive. The adjective use is more likely.

2. She kept her promise that he would visit her aunt regularly.
She - subject
kept - main verb
her - possessive pronoun, modifying "promise"
promise - direct object
[that she would visit her aunt regularly] - noun clause. Since noun clauses cannot be used as adjectives, then this must be an essential appositive to the word "promise."

Noun clauses, appositives, and essential/non-essential elements in English are not always easy to understand or to identify!!