Although I can't find a link for this couple I think this could be a possible for the parents of Mary McIntyre.
There was a Daniel McIntyer/McIntyre m Janet White in Kilwinning,Ayrshire 9th August 1823, and although I can't find any children that's not uncommon for the time.
I found an 1861 Census return for a Thomas Shaw and wife Mary in Kilwinning, listing 5 children -John,Daniel,Thomas,James and Marion,
but they had already lost a daughter in 1858 aged 3yrs called Janet.
So if Thomas's parents were John Shaw and Janet Thomson, I wondered if they had followed with traditional Scottish Naming.
1st boy named for Fathers Father, that would be John.
2nd boy named for Mothers Father, that would be Daniel.
1st girl named for Mothers Mother, that would be Janet.(which would satisfy BOTH Grans).
Not my clearest ever explanation,hope you can follow it.
Thought it was worth a mention.
Young Thomas born in BRAZIL so already far travelled,and no record of family after death of young James in 1864 to Hydrocephalus.