Looking at the whole picture with what you know (which is little) & what is commonsense.
Being Ivy was born illegitimate out of wedlock with Janet changing her surname to Mrs Thompson, its possible Janet never baptised Ivy or the church shunned her, then who would look after the baby while Janet earned a living as a Milliner?, last! I think the law would have been made in law all people and children are named on shipping passenger lists both sides of the Atlantic in
case of disaster at sea.Maybe Janet made a trip back to England between say 1896 to 1900 or collected her after marriage to William Caldwell, and being the person who brought Ivy up 1891 to 1900 still had Ivy on the 1901c census.
Therefore look at passenger lists post 1900.
