Despite what they believed or what they were told, John YATES could not have been the father of the three youngest children if he died in 1868. Louisa may have been their mother, but I would also be looking at them being the children of one or more of her oldest daughters.
Even if the births weren't registered it is highly likely that they were baptised, so the Bendigo church registers may help to sort them out.
The Bendigo Family History Group has been indexing church registers:
http://www.bendigofamilyhistory.org/ourdatabase.htmDebra