Ive had a wee look on the Census, and found Ambrose Burnside of Durham, a Hawker in 1891. I also found him with wife Isabella in 1861 still a Hawker in Durham. I am assuming you already have these - So I thought who was Isabella?
Ambrose Burnsides married Isabella Gordon Jan-Mar 1849 Easington Durham GRO Ref: 114/24
Ambrose gave his place of birth in the census as Yorkshire
There was an Ambrose Burnside baptised at Deighton By Northallerton Yks 05.07.1829 s/o Edward Burnside and Sarah Waddington. (This is taken from the IGI which of course is not a fully comprehensive list, so its possible this isnt your Ambrose. I think it is though - see below!).
Now Edward Burnside and Sarah had a bundle of kids at Guisborough, which is where Ambrose thought he was born according to the 1861 census (a nice big clue there).
Mary c.12.10.1831
Benjamin c.07.11.1834
Sarah c.14.03.1840
Isabella c.19.01.1843
Joseph c.06.06.1846
So I thought, what are the others occupations?
Benjamin married Dinah/Diana Lindsley and lived at Chester le Street, Durham, where he was also described as a hawker.
This led me to find Edwards family at Guisborough in the 1851 census:
Edward Burnsides 50 Lic Hawker Tackley? Durham
Sarah 47 Bradford Yks
Mary 17
Benjamin 15
John 12
Sarah 10
Isabella 7
Joseph 3 all born Guisborough.
Interestingly, next door are a few Wilsons described as Tinker/Tinman as well as an Isabella Clark and a Bridgett Moss, Vagrants.