If Anna resided in the US for only 3 years then of course there would be no Naturalization found as the residency requirement was 4 years.
Where did this family live in the US?
You mentioned one of them Naturalized in one of your other messages. Which one? Whered did he live. The Naturalization record may give the birth location and ship and date of arrival.
Have you even looked for a ship manifest? MUELLER is a common name and between 1883 and 1887 thousands with this name came to the US.
MUELLER is likely an Americanized spelling, the German spelling may have been Müller
It was the norm for the man to come to America first (in fact most immigrants did not intend to stay here, their goal was to earn enough money to go back home and buy land) and then for the wife and children to follow