The date of emigration from Bohemia to the United States would be between 1854 and March 1858. 

Julia Mohelnicky/Mohelnitzky Klein gave the year of her immigration as 1854 in the 1900 census and 1910 census.

The Anton Mohelnicky/Mohelnitzky family do not appear in house records in Sedlcany, Czech Republic after 1854.

Records show that Anton, Julia and Mary Mohelnitzky were admitted to orphanages in Milwaukee, Wisconsin, in March 1858.

Maybe the family appears in the New York Passenger Lists, 1820-1957. Using Ancestry.com' search forms, I was unable to find the family. The passenger lists were badly transcribed and the name may have been misspelled or omitted by transcribers. One could search page by page, beginning in 1854.

Bremen passenger lists have been destroyed: 

"The city council of Bremen passed ordinances in 1832 that required companies transporting emigrants to file a list of all passengers with the city's emigration department. These contained emigrants' names, ages, occupations, and places of origin. Between 1875 and 1909, the passenger lists dating from 1832 were destroyed by city archivists for lack of storage space, and the lists covering emigration during the years 1910-1920 were destroyed during Allied bombing raids on Bremen during the Second World War."

Here's a handy guide for what to look for in the ship passenger lists:

Last name: Mohelnitzy/Mohelnicky

Name      Born         Age in 1854
Anton      1818         36
Maria      1822          32
Anton      1848           6
Julia         1850           4
Marie      1852            2

Maria could be Mary
Julia could be Julie or Juliana
Anton could be Anthony, Antonin, Tony
Or they could just have first initials.

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There are several family stories about the immigration. In each telling, the story varies:

• "Anton Mohelnitzky came to America with his mother and father and two sisters Mary and Julia. On the way over, the father got sick and died when they got here. The mother married again and put the 3 children into an orphanage (other story--the mother died of a broken heart)."
  
• "At the age of 9 he (Anton) and his 2 sisters were sent to an orphanage, Mary and Julia. The 2 girls were adopted and brought to America and he at the age of 19 set out to look for them in America. He found them in Milwaukee, Wisconsin, and was allowed to see them but forbidden to say he was the brother."
• "Anton Mohelnitzky came from Bohemia with his mother, to Milwaukee. His father had died previously in Bohemia. The mother got sick and had to go to work. She couldn't keep the children (Anton, Julia, Mary) and put them in an orphanage."
•  "Anton Mohelnitzky (father of Anton Mohelnitzky) died on the ship on the way to America. He died at sea and was buried at sea."
•  "...my father was born in the United States. His father was half-Bohemian, and my grandfather on my father’s side, he was an orphan."

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Reasons for emigration of German-Bohemians in the late 1850's*:

"The primary reason was that the Austrian Empire was being combined with the Austro-Hungarian Empire, which was raising taxes significantly, and increasing the overall threat of war in the region.

In addition, Bohemia had a comparatively high population density, so many Bohemians were worried about opportunities for their children. 

There were also large divisions in the church, which was a huge part of most Bohemian's lives."

Source: ?

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Leo Baca books of Czech Immigration

I checked all 9 volumes, specifically these 3 volumes for any Mohelnitzky/Mohelnicky or variations thereof and found nothing:

Czech Immigration Passenger Lists, Volume I (Revised)

Galveston 1848-1861, 1865-1871
New Orleans 1848-1879

Czech Immigration Passenger Lists, Volume IV(Revised)

New York 1847-1869
1525 Czech names added

Czech Immigration Passenger Lists, Volume VIII

Baltimore 1834-1879

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