Re: Antonina's responses on the ship manifest:
Yosef Laurinawicz was in Russia (looks like Wersa - Kowno, to me) There's no evidence that he was in the US. His name was given in response to:
"The name and complete address of nearest relative or friend in country whence alien came"
Wincenty Proszogulowicz's name was given in response to:
"Whether going to join a relative or friend; and if so, what relative or friend, and his name and complete address"
In this second response she says Wincenty is at 132 Jefferson St., Trenton, NY -- which matches Wincenty's manifest and the 1912 city directory.
Take a look at the manifest at the Ellis Island site. It has slightly better quality than the one here at Ancestry.
Sorry - I didn't catch it earlier when you said she was going to her brother's in the US -- She was leaving her brother behind (so to speak.)