I have just learned through research at the US Library of Congress the following information. Some of what I posted earlier is in error. Information from Max about his entry into the US came from his Naturalization form which was done in 1941, 48 years after he arrived, and his memory was faulty as he was only 7 years old at the time.
Herman alone came to the US in 1892 arriving on July 22, 1892 traveling from Hamburg on 30 June, on the Augusta to England. From there he departed from Southampton on the Victoria, arriving in the US at the Port of New york.
His wife Ida and the five children traveled to the US in May 1893, not '94. Their ship was the Wandrahm, and it was not sunk, but ran aground off Apple Island near the city of Quebec on May 16th, and from there it was towed to Brooklyn, New York, arriving on May 23rd, using the date that Max had on his paperwork. Rather than Adolph and Martha coming to Chicago with him in 1892, they all arrived together some time in late May, early June 1893.
(An article about the events surrounding the controversial method of towing the ship are published in the New York Times of July 28, 1893, and include information about the towing ship, the tug tender, and the travails of the travel. What is not clear at this time is whether or not the passengers were off-loaded in Quebec, or continued on the ship to New York as it was being towed. More to come on that later.)