Mary Collins, according to death certificate, was daughter of William Collins and Ann Hendry. (Marriage certificate states that mother was, what looks like, Agnes Henry!!)
William Collins and Ann Hendrie married 30/12/1859 High Church, Glasgow. Census shows both of them were born in Ireland.
Mary Collins was born 17/5/1863 Shettleston, dau. of William Collins and Ann Hendry.
This makes Mary 15 1/2 when she married William Taylor on 27/12/1858. I believe this perfectly legal in Scotland.
As to William Taylor, b.1858 son of Charles Taylor and Agnes Cooper.
According to 1861 census in Hamilton they were not married. I am only able to view transcripts and it says:
William Steven 41 Silk Weaver b. Hamilton, Lanarkshire
Elisabeth Steven 58 Tambourer ditto
Agnes Cooper stepdaughter 32 unmarried Tambourer b.Hamilton
Alexr. Taylor grandson 8 b. Hamilton
William Taylor grandson 2 ditto
This seems to be an accepted thing in Scotland - that children born illegitimately more often than not would grow up with the surname of their father. Sometimes you will find that both parents are named on a birth certificate even though not married, sometimes not.
In this instance, William's birth is registered under mothers maiden name and his father is not named:
William Cooper b.1/11/1858 Hamilton, son of Agnes Cooper.
As you can see from 1861 census, it looks like Agnes had had an earlier child by said Charles Taylor too.
Annette