You kindly supplied a lot of facts; thank you for listing the details. I haven’t yet absorbed all of the details; apologies if it was mentioned…
You stated: “…She has a mother, brothers and sisters to weep after her in the Old Country, and a kindly good natured husband in this place, as well a brother of the grieving husband, who set up home with them here…”. Have you searched for and found the brother’s arrival? Again, sorry if you mentioned it.
The first passenger list that I found for a (an incorrect) Louisa Jones was almost impossible to read. I wonder if your Louisa’s list might be in the same condition which could explain why she has not yet been found.
As mentioned, she could have sailed to Canada. Quite a number of folks did sail to Canada even though they intended to live in the states (I’ve read that given the ties between Canada and England, it was “easier” to go that route).
I would imagine that you’ve searched for William’s arrival, but asking anyway.
Don’t discount errors in passenger lists. While looking for my Mumford ancestors, I found a married couple on a passenger list, but their birthplaces were recorded as Ireland rather than England - but, I am almost certain that they were my James and Susanna.
I will continue to follow this topic (later today).
Added: Louisa could have sailed under the name of Mrs. W. Jones, which could hamper the search for her.