There aren't too many Killians or similar names in Griffith's Valuation of Westmeath (1859).
https://www.rootschat.com/links/01prb/I found a James K but he was only renting land, not a house. But there was a Mary Killian renting land, buildings, and a house in Dysart Townland. The land that James K was renting was in Rathnamuddagh Townland, which is not far away. So maybe James, the father, died and Mary was the tenant on the lease. If so, maybe the James that was only renting land was her son James, and he was living at home.
IF that is your family, then James would the one mentioned in Bridget's obituary.
The problem is that Dysart Townland is probably in a different parish, Dysart Parish, not Mullingar. I don't know for sure, someone more familiar with Westmeath would know.
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I found another daughter in the family, Julia, baptized 29 April 1830, in Mullingar. The index gives the mother's maiden name as Keennan, but the image says Kiernan.
And you have Bridget, baptized 30 August 1826, in Mullingar?
I didn't look for others, there must be some in the mid 1830s.
A tree at ancestry says that James Scott was born in 1822 in Dysart, Westmeath, and that their first daughter, Mary Ann, was born there also, in June 1849. But there is no source for the information. Sometimes facts like that get passed down in the family, but sometimes on ancestry they come from misinformation. But Dysart would make sense so far, anyway. Here is the link in case you have a subscription:
https://www.ancestry.com/family-tree/person/tree/32424843/person/390147593868/factsI've got something on the US end of things, but will post that with your thread over there.