A lot of old B & D records record only the father - as if the mother had nothing to do with the person being here!
The first part is true of early baptisms (mostly pre-1800), but we are talking about the 1870s here.
The reason mothers may not have been recorded in early records was not necessarily because mothers were thought to be unimportant or irrelevant. Families were in general headed by males, so when the records were taken it was sufficient to simply record the father. Adding additional information like mother's name served no useful purpose at that time. Remember that records were not kept to appease future family historians. I'm not saying it was fair or right, just let's be careful not take things out of their historical context.
Sorry to digress...
As I say, we are in the 1870s in this case, and the vast majority of baptism records from this period name both parents. In this case I wonder if it may be that the mother was not Catholic, or she was not present at the ceremony so her details were not entered, or simply not known when the register was completed? I'm sure there are other perfectly innocent reasons as well.
It might be that the birth certificate for that Jane may be the only way to work out which Jane is yours - and even then there's no guarantee that it will help.
Alexander