Hmm.
1861 census says Jane Williamson was born in Glasgow. 1871, 1881 and 1891 say Jane McLaren was born in Kilmadock

1871 Census lists Daniel McLaren; wife Jane, 40; eight children who are presumably Daniel's by a previous marriage, one child of both, but no 13-year-old George and no 10-year-old William Williamson. William Williamson, mmn Peel, died in Bridgeton in 1861, but George W, mmn Peel, 59, died in Springburn in 1922.
She died in 1904, age according to deaths index 62, mmn Moore. That suggests a birth in 1841/1842, so it's probably wrong.
There are two more deaths of Peels, mmn Moore.
Margaret, aged 74, 1907, in Kelvin, other surname
WilliamsonElizabeth, aged 73, 1916, in Garngadhill, other surname Telford
Margaret Peel married John Burton Williamson in Bridgeton in 1859, and they had at least 5 children: John 1862, Elizabeth 1864, Ann 1866, Alfred 1869-1869 and Margaret 1870-1872.
Elizabeth Peel married John Telford in 1879 in Dennistoun. They don't appear to have had any children.
It might be useful to look at Margaret's and Elizabeth's marriage and death certificates to see what their mother's name was.
1851 Census in Glasgow: Isaac Peel, 40, born Belfast; wife Constance, 38; daughters Jane, 18; Margaret, 16; Ann, 7; Elizabeth, 7. Could these be Jane and her family?
What are the names of Jane's parents, according to her marriage and death certificates? In 1861 in Glasgow are John Williamson, 38; wife Margaret, 28; daughter Jane, 7; and sisters-in-law Ann and Ely Pall, both 17.
Could John have been a brother of the elusive George? John was aged 47 in the 1871 census. In 1881 in Glasgow are Margaret Williamson, widow, 50, with son John, 19 and daughters Elizabeth and Anne, 19 and 15.
What about George W c1857-1922? In 1881 in Glasgow are George W, 24; wife Annie, 22, son Andrew, 3 and
stepson David McLaren, 10. As Annie was clearly too young to be David's mother, this must surely be an error for stepbrother?
George W married Ann Major in Dennistoun in 1880. There's a birth of Andrew W in 1878, mmn not indexed, and births of George W in 1882 and James W in 1884, mmn Major. All three of these boys, plus an Annie Thompson Williamson with mmn Major, died young. Ann Major or Williamson, mmn Thomson, died in 1881 aged 29. George W married Elizabeth Anderson in 1890 and they had at least 5 of a family, including Daniel, born 1890.