Did you mean Margaret Robertson Paterson and not Elizabeth? I found passenger list entries which match the information you provided about William but his wife's name is listed as Margaret on the passenger lists. There is a marriage registration at ScotlandsPeople for a William Hamilton marrying Margaret Robertson Paterson in 1918 in Shotts, Lanark.
Here is the passenger list entry for William Hamilton arriving in Quebec aboard the Montclare on 6 Jun 1926 as follows:
William Hamilton, 30, born Wishew, occupation police constable, destination Police Headquarters, Toronto. In the column asking for the name and address of nearest relative in the country from which he came, he listed wife, Margaret Hamilton, 20 Victoria Street, Harthill, Scotland.
Here is the passenger list entry for Margaret with four children arriving in Montreal on 23 Apr 1927 aboard the Melita:
Mrs. Margaret Hamilton, wife, 30, born Harthill, Scotland, going to husband, Mr. Wm. Hamilton, Swift Current, Saskatchewan. In the column asking for the name and address of nearest relative in the country from which she came, Margaret listed mother, Mrs. J. Paterson, Victoria Street, Harthill.
Since there is a possibility that the children listed could still be alive I won't post the details about them.
If you would like copies of the passenger lists, please PM me your email address and I will send them to you.
Jacquie
Edited to add: I've received a PM from sicknote and he confirmed he meant Margaret, not Elizabeth.
