Elizabeth McPheat or Hunter, mmn Gillespie, died in Edinburgh in 1914 aged 54. Noting that her first daughter was named Barbara Gillespie, she has to be the daughter of William McFeat and Barbara Gillespie. I can't find her birth or baptism, but three younger siblings were born in New Monkland; Thomas 1855, John 1857 and Margaret 1859.
Elizabeth, 7, is the sixth of nine children to William McF and Barbara G, listed in New Monkland in the 1861 census. The three younger ones are as listed above.
Annie McPheat married Alexander Hunter in 1897 in New Monkland. There are four deaths of Hunters, mmn McPheat, born 1897 to 1917. One of these was William Easton Hunter, aged 85, in West Calder in 1983. There's a birth of William Easton Hunter in Bathgate in 1898.
In the 1901 census in Bathgate are Alexander E Hunter with wife Annie, 30, born East Longrigg with William, 3; Annie 1, and Jeanie McPheat, sister, 12, born East Longrigg.
In 1891 there's a family in New Monkland including William McPheat, 40, born New Monkland, with wife Annie and a whole string of children including Annie, 20 and Jane, 2. They are the family of William McPheat and Annie McMillan. There's also an Edward, which is useful because it is not one of the commonest names in Scotland and it occurs among the other Hunter children.
In 1851 there is a six-month-old William McFeat in the family of William McFeat and Barbara Gillespie in the census in New Monkland.
So I think that Annie McFeat/McPheat, wife of Alexander Hunter, was the niece of Elizabeth McPheat/McFeat/McPhite, daughter of Elizabeth's older brother William.
Do not, however, take this as certain. I could easily have got it wrong. You must check it out by getting the two Hunter/McPheat marriage certificates and the marriage certificate of William McFeat and Annie McMillan.