Here's some additional information on the US side, to save some effort.
Hector Darling died about 1865, Mary Ann remarried in 1867 to Jesse Hightower in Hunt County, TX. It is assumed that Mary Ann died before 1870 as Jesse is living with his daughter Margaret and Mary Ann is nowhere to be found.
I have found families of John and William Craine in New York later on, but haven't found anything yet to connect them to either Mary Ann or the family arriving in 1834.
I have nothing to substantiate my Mary Ann being the Mary Ann who arrived in 1834; it's just my best guess at this point. Based on the little I know at this point, she could have arrived in the US at any time after her birth and before the birth of her son William.
The death certificate for Mary Ann's daughter Frances shows Mary Ann's maiden name as Crane, but it's about 70 years after the death of Mary Ann, and I'm accepting any spelling at the moment.
I'm casting my net pretty wide including the arrival in 1834; it's entirely possible that it's a completely different family, but it's a place to start. Thank you very much once again for the additional information. I'll take a closer look from my end.