When can auxiliary "have" for a past participle in a modifier be omitted?

There are two ways to write this sentence. 1. Arrived at the church, she would stand looking down between the columns. 2. Having arrived at the church, she looked down between the columns.

Here we have an adverbial clause, describing the state of things while she is looking down between the columns. In this case, the state or her position is that of her arrival to the church, where she is when she looks down between the columns. Here is another example.

1. The child, located by the rescue dog, was reunited with his parents.
2. Located by the rescue dog, the child was reunited with his parents.
3. The child, located by the rescued dog, would stand there wondering if they were not far behind him.

In this case, the adjective clause describes which child was reunited with his parents. He was the one found by the rescue dog.

The sentence, written in the third way, is sometimes used when narrating a story, especially in a TV program about life and death.

"The man, beneath the bolder and suffering from the cold, would spend the next ten days without food."

So returning to the aforementioned excerpt from the novel, if we rearrange the sentence to read less awkwardly, it could be written as seen below.

She and Wanda, arrived at the church, would stand looking between the columns.

Grammatically, the original sentence doesn't violate any rules, but likely your English teacher would mark it in red and ask you to revise it.

A few other examples: The couple, newly wed, will begin their honeymoon tomorrow. The man, deceased, left his will to the youngest child. The apple, eaten by the worms, would decompose over the next ten days.