Robert,
Mabel’s birth & 1 of her brothers:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1907/01691/1671716.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1905/01788/1702283.pdf
Steele family in 1901:
http://www.census.nationalarchives.ie/pages/1901/Londonderry/Ballymoghan/Ballymoghan__More_/1532012/
And 1911, at which time they had 8 children, all still alive:
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Cookstown_Rural/Cookstown__Part_of__Rural_/857932/
Parents marriage in 1895 (note Samuel had been married before):
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1895/10514/5829744.pdf
Samuel’s first marriage:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1888/10765/5926106.pdf
1st wife’s death in 1889:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1889/06145/4755618.pdf
1911 census contains Elizabeth Steele. Here’s what looks to be her death in 1919, informant was her brother Samuel. The family was living in Tamnadace (Tamnadeese) then.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1919/05146/4418389.pdf
Daughter Maggie Steele married Dixon Hogshaw in 1916:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1916/09793/5554939.pdf
Daughter Selina Steele may have married Lewis Young on 24.4.1928 in Belfast. That marriage is viewable on the GRONI website for £2.50.
You can contact Sylvia Anne McClean on Ancestry by clicking on her name. That takes you to the messaging option.
I can see William & Mabel on the Doric departing Belfast on 4th May 1929 (immigration records on Ancestry). Their address is Ballymoghan, Magherafelt. His occupation farmer.
I had a look on the GRONI website for William & Mabel’s marriage 1921- 1929 in Northern Ireland but cannot see it there. I also looked for a William Mooney born c 1902 in the Magherafelt area but there weren’t any. Nor anyone likely in the 1911 census. No Mooney families in Ballymoghan More or Ballymoghan Beg in the 1911 census. There were plenty of William Mooney births elsewhere in Ireland but without knowing his parents names it’s a needle in a haystack. Perhaps you can find his death certificate and get parents names from that?
I searched the Valuation Revision records for Ballymoghan 1915 – 1929 (they are on the PRONI website) but did not find a Mooney household there in that period. I did however find a brief item in the Mid Ulster Mail of 6thSeptember 1924 about William Mooney of Ballymoghan who had been fined 5 shillings and costs for breaching a curfew. He had been with a Joseph O’Kane of Ballyheifer and the explanation offered was that they hadn’t known the time.