
I've just found a Janet Brown in a crew list going to NY
Age 30
Birth Year abt 1867
Birth Place Liverpool
Event Date 1897
Port of Registry Liverpool, Lancashire, England
Ship Name Lucania
Looking at the image, the whole line is crossed out with an entry about being transferred. Possible March 1897. It doesn't say where transferred to, but there is no signature unlike those who sailed. But there is an address 149 Stanley Rd, plus an illegible (to me) town or area, could be Bootle, and the job of Stewardess. There are hundreds of pages of images and I have yet to find exactly when the ship sailed but as she wasn't on it, no matter.
I've started looking at passenger records for Janet Brown or Caldwell to/from the USA over a range of years because she could have left Ivy in England with grandmother and then returned to collect her later, as suggested by a Rootschatter earlier (think it was you Sandra). So if Janet Caldwell is with her brother in 1901 (when she wasn't visible in US censuses) that could have been the reason for the trip. Although there were only a few years between her brother and her so can't see why her age would be so wrong. I need to pursue a mother in law Janet Caldwell as you suggested.
There might well be a William Caldwell who stayed in England, but he was cited as Ivy's father on the birth cert, if we could ever find her birth!