Excellent question - on which I have often pondered. 
No relation. However, my father did take his Globe of Death to Margate in the 50’s and 60’s. I have a photo of him building the Globe in Dreamland. We believe Yvonne may have amended her surname to capitalise on the ‘Staig’ legacy. Infact, a rider in the late 1940’s did infact change his surname to ours: ‘Staig’ precisely to take that advantage. He was not a nice man (con man springs to mind). First name was Ernie and put it about he was my father’s brother - he wasn’t!
In fairness, I cannot be certain re the Yvonne Stagg story but bit of a co-incidence?