Jimmy_c
Many trees are copied without having been personally researched with certs purchased and records scrutinised, etc.
Because there were so many Joseph Clarkes born around the same time it is hard to find the exact one.
The one positive is you have the marriage cert for Joseph and and Ivy presumably from whom you descend.
But what you need is the birth cert of the Joseph Clarke either Notts or Staffs or wherever.
Or a baptism record of same. That will give you Mary,s surname.
These no one seems to have. None of the trees has an image of birth cert or baptism As you say the only thing is 11 July.
If Joseph,s father was a military man then Joseph,s birth may be on the gro military birth site.
I found my mother.s birth this way when it was not on any other.
Naturally I knew her birthday but I could not find it to obtain cert except in Gro overseas section.
You could request a search . It used to cost £4 , probably more now.
Sometimes going sideways yields results...hence maybe tracing Patrick or whoever Joseph,s older sibling was.