This reply is overdue but I wanted to let you know that your information about the probate paid huge dividends for me!
The will of Annie Kosowszyer stated that she was also known as Annie Genik. The executor of the will was my grandfather and the will also stated that my great aunts were her children.
I found an entry on The Ship's List (the Arcadia) for Annie Kosowszyer and her two children. She was on the same ship as Nykola Genik and Rozi and John Pedlisesski (and their children).
I found a death certificate for the younger of the two children shortly after they arrived in Manitoba (early 1898). The place of death for the child is Rozi and John Pedlisesski's farm. I believe the older child died on the ship - or maybe shortly after - he seems to have disappeared.
So I believe that Annie came to Manitoba with her 2 children and lived with her relatives (John may have been a brother or cousin as her maiden name was the same as his). It is possible that her husband came to Manitoba before she did but I can find no death record for him in Manitoba. So it is also possible that she was a widow when she left the Ukraine. Once her children from the unknown Kosowszyer marriage had died, she moved to Nykola Genik's house (she is listed as his boarder in the 1901 census).
So there are two things I would still like to know but likely will never know - was she related to John Pedlisesski and how. And what happened to her first husband?
Lastly - I can't find her in the 1921 census. I assumed she was living in Dauphin but she is not showing up anywhere. Any suggestions?