I'm just posting this comment as I'm not sure if you were aware of one bit of information with regard to the 1912 travel record. On the US incoming manifest noting Ada's arrival on the Kroonland on 21 May 1912, there is a comment that Ada is returning to her home at 414 Rutger Street in Utica, New York. There is no one near her name on the manifest that would seem like a relative/friend heading to a similar/nearby location.
None of the other posts I read seemed to mention this location, and so I thought you might find it helpful to your research in case you are aware of other relatives living in the area or a reason Ada might have lived in New York at the time even though her family seemed to be in either Illinois or England. Also, it looks like Ada appears on the 1911 Census, and so maybe her occupation there (if there is one) is something similar to what she was doing in New York.
Your best bet to learn Ada's fate may be to track down an obituary for one of her parents, as it would hopefully note Ada's married surname or else mention if she predeceased them.
