Hi there,
Its not impossible to have 18 children by the same wife ... several of my 19thC family managed 19 and 20, with a couple of multiple births. But of course with that very popular surname of SMITH ... well I would not just rely on the census records or even on the IGI extracted ... I'd be wanting to obtain actual certificates which should show lots more information about the family ... for example marriage should have the names of the groom and bride's parents, occupations, addresses, ages etc ... You have Clara Miller marrying a George Smith at All Saints, Birmingham, Warwick on 11 August 1872 ... but how do you know that it was 'YOUR' George Smith ...

... Clara Miller may have been an aged widow that Geo married for her money and no children were born to them .. or she may have been say 16 and therefore had 18 children over the course of the next thirty years or so... That extracted IGI record doesn't give the ages of the couple. Sorry, but in my humble opinion the surname of SMITH definitely means you will need to dig deeper and spend some pennies on certificates rather than relying on several census records before even considering Clara Miller was your Geo's wife...
Some positive thoughts :
Have you checked out the pilot site
http://pilot.familysearch.org/recordsearch/start.html#start and also these births and the marriage would have been registered so have you checked this link
http://freebmd.rootsweb.com/ ... (you can get the GRO references on that link)
Have you any of the birth certificates for the children .. perhaps say Alonzo ... hopefully as this is not a popular name he may be easier to trace.
Have you looked for Medal Cards for the sons ... tespecially the younger ones .. they were the right age to have served in WW1 ...
Have you asked for a Scavengr Hunt here at RChat? Here's the link for that
http://www.rootschat.com/forum/index.php/topic,358572.0.html May I suggest you send a PM to have your hunt reserved for you, there's some very experienced RChatters who regularly help other RChatters to break some brickwalls...

Others may have more ideas, I'm NSW Australia based, so my understanding of UK records is not as reliable as the UK Rchatters..
Good Luck, I've a couple of SMITHS in my tree

Cheers, JM