Hi Katerisingsun.
I have been trying to give your problem a bit of thought but I don't seem to be getting close.
The earliest marriage of a Patrick Flaherty to someone called Honoria in Galway,I can find was in 1854 the details are:
23rd October 1854 at Tuam Patrick Faherty married Honoria Corlis (or Corly)
http://registers.nli.ie//registers/vtls000632080#page/1/mode/1up This would only work if Thomas Michael Faherty's mother died and his father Patrick Faherty remarried to someone called Honoria.
With regard to the baptism of Thomas Michael Flaherty, to a father called Patrick in the period 1847 to 1849 The only record I can find is:
Bapt August 1848 Thomas Flaherty Father Pat Flaherty mother Cath Moran at St Nicholas North & East , Galway City.
http://registers.nli.ie//registers/vtls000634217#page/1/mode/1up I cannot fit a Mary Flaherty into the sequence although there is a baptism if a Maria Flaherty father Patrick Flaherty mother Catherine Moran on 31st January 1845 but that took place in Loughrea, Galway
http://registers.nli.ie//registers/vtls000632950#page/1/mode/1up The above Maria had a brother Michael also baptised at Loughrea father Patrick Flaherty mother Catherine Moran on 10th August 1846.
http://registers.nli.ie//registers/vtls000632950#page/1/mode/1up There is also a baptism for a Thomas Flaherty 12th January 1846 at Tynagh but the father is a Martin Flaherty with a mother called Honor Mulkern
http://registers.nli.ie//registers/vtls000632962#page/1/mode/1up I do not think the above is what you are after but I thought it worth recording my efforts!!
Sorry I cannot be of more help
Regards
The Wirral Way