Hi Julie,
I'm afraid I don't know the date of Ambrose Burnsides death. I looked up the BMD on An***** and found an entry for a Ambrose Burnside: Age 60, 1st Quarter 1884, Vol 10a, Page 134.
But....Isabella and William got together between 1871 and 1881, Isabella was living with Ambrose and their children in Durham in '71, and living with William Cunningham at Vinegar Hill, Glasgow, in '81.
I think I will have a quick look at the 1881 census for Ambrose to see if he was still alive then, I've just assumed that he was dead....you know what assume does in this game

.
I have the original death cert's for William and Isabella and they both mention their prev' spouses, but I could not find a marriage for them in SP, so I think they married in England.
This is side tracking from your original question, but you never know what helps.
I'll get back to you if I find anything more.
Jane.