Below, is this your Martine? Buried at Lone Rock Cemetery, Flandreau, Moody, South Dakota, as Marthine Skjeggestad Gunderson, parents noted as John G. and Ingeborg Skjeggestad? (John and Ingeborg buried same cemetery)
It would likely help to clarify when and where Kari and Lise were last seen.
Are you saying you located Kari and Lise in Ontario? Or are you saying your last record of them is their arrival in Quebec? (You ask is it possible that they died in quarantine, but you also say you can "follow them to Ontario." Confusing) Does your family story about Martine suggest how old she was when she was sent to La Crosse? She was sent from somewhere in Ontario (by whom? when? where in Ontario?).
from Police Emigrant Protocol and Passenger List
Departed Christiania 26 April 1873
Arrived Quebec 04 June 1873
on the bark "Edda"
Captain A. Andersen
Iver Olsen Skjæggestad age 60, Farmer, residence Gausdal - died May 12th
Kari Simonsdatter Skjæggestad* 60 wife, residence Gausdal, destination Ontario
Lise Iversdatter Skjæggestad* 25 daughter, residence Gausdal, destination Ontario
Martine Iversdatter Skjæggestad* 2½ daughter, residence Gausdal, destination Ontario
Here's a link on Wikipedia about Grosse Isle, where immigrants arriving in Quebec were quarantined if need be:http://en.wikipedia.org/wiki/Grosse_Isle,_Quebec
This article says only 42 deaths are reported on Grosse Isle from 1870 - 1880 but doesn't tell how to access those records.
Here is the story of a woman who died at sea but was buried in Quebec:http://boards.ancestry.com/thread.aspx?mv=flat&m=12362&a...
In general, it often helps when one allows the records to speak for themselves and tell the story. At the moment I can't quickly pull up John in South Dakota census (though I think I've spotted him on Find a Grave) and seems silly to hunt longer when you obviously have already identified him and Martine there. Since you don't know when or where you lost Kari and Lise, every part of Martine's story might be relevant.
Who is Carl Skogstad - do you know? Is his name possibly an Americanization of Skjeggestad? There's a Carl Skogstad buried in Flandreau, South Dakota. There's also a Mathea G Skogstad buried same cemetery as John G. Skjeggestad (Lone Rock Cemetery in Flandreau), and cemetery notes her as born in Gausdal. Was this John's sister, do you know? Or if not, who was she? Do you know of other siblings to either John or Lise who immigrated to Ontario or anywhere in North America (their locations would be possible locations for Kari and Lise).
If Lise and parents and daughter Martine were en route to join John, there might be a record of them at Lone Rock Church (or at any earlier location where he is found). At least so far, your story doesn't include anything that suggests the family was not going to John. If Lise and her parents all died, leaving Martine a toddler, one could guess that John might feel ill equipped to care for her on his own and send her to family or friends until he could remarry or until she was older. In other words, could the family be near John before Martine went to La Crosse?http://southdakotagravestones.org/view.php?id=42349
Map of Canada in 1873:http://www.canadiangeographic.ca/mapping/historical_maps/187...
Thanks in advance for your patience with all the questions.