Thank you Betty for all your help!
I do have that information about Elmer, Elizabeth and the children. In the 1920 census, 2 of their boys were in the agricultural school near Rochester, NY. I am guessing with his wife gone, Elmer could not handle all 5 of the children alone.
I thought that maybe if I could figure out how the immigration records worked- where they are located, how I would go about finding them, etc. I would be able to see when she first came to NY, and if she ever crossed back.
If she wanted it kept a secret back then, she could easily have crossed at the thousand islands, a simple thing to do by boat.