You have everything figured out, albeit by using literal translations.
The 'los' in the 'los ojos' phrase is simply an article. In Spanish, when someone's eyes are obviously belonging to the subject, the article is used instead of the possessive adjective.
In other words, to say "She, with tears in her eyes," the correct grammar calls for 'los' (the article) instead of 'sus' (the possessive adjective).
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