It is a very convoluted family, and with Craine's on both sides adds to the confusion. I think the following might help Mary understand why Lucy cannot be the mother of Margaret Killip nee Craine.

First, because she was a Craine, she would have been another illegitimate child born about 1823, before Lucy's marriage to John Quay. There is no baptism on the IGI to match, though of course a detailed search of the registers is needed to confirm.

Second, and more importantly, the 4 children of John & Lucy Quay on the IGI are:
1. Margaret bp 1830 Braddan
2. Margaret bp 1834 St Barnabas Douglas
3. Manassa bp 1836 St Barnabas Douglas
4. John bp 1844 St Barnabas Douglas

The two sons show up on the census and Manasseh is Mary's ancestor. The two Margarets seem to disappear and aren't on Brian's burial index either (but neither is Lucy). But the fact that they existed at all would preclude there being an earlier Margaret dau of Lucy who lived on to marry.

I wonder if Margaret was the spokesperson for the 1871 census and she mentioned her "mother in law" Lucy Quay, and the census taker wrote it down just as she said. The different last name would make him not question it.