Were they corn millers?

Sorry, couldn't resist. Maybe contemporaries joked about his name and Corny junior decided he would be George instead.
Middle names weren't common then for ordinary folk. Did George/Cornelius have an elder brother named George or Cornelius who died?
Sons were usually named for grandfathers, father and uncles, following a traditional naming pattern. Occasionally a person changed their name at the request of or to honour a well-off relative or benefactor, perhaps for inheritance purposes. Was there a grandfather or uncle George? Perhaps his parents couldn't agree on his name.
What name was in 1793 baptism register? Was it Catholic or C. of E. register? He may have been in both as non-Anglicans were recorded in C. of E. parish baptism registers at the time because 1) there was a tax on births and 2) C. of E. clergy kept records of Catholics in their parish for administrative purposes - Returns of Papists &c. Although penal laws had been relaxed a few years previously, Catholics were still subject to some sanctions; they weren't equal citizens. It was almost 40 years before the Catholic Emancipation Act was finally passed.
Was George or Cornelius on marriage register? Did he sign his name?
Were Caroline and John baptised in a Catholic church? Were they baptised on the same day?
It's possible that George/Cornelius used alternative names according to circumstance and so he could get on in life. George was a patriotic name. Did he join the army at any time? He was born at the start of the wars against Revolutionary France which lasted until 1815 (Waterloo). There was some suspicion of Catholics at the time of the French Revolution (1789) as Catholics in Britain had been regarded as "the enemy within" for more than 200 years. Catholics had been officially allowed to join the British Army only a short time before. Promotion was restricted. I've got a Catholic captain in that war.
Penal laws were slightly different in Ireland and Scotland from England and Catholic Relief Acts didn't happen simultaneously in the 3 countries, causing confusion for natives of each country visiting or residing in another e.g. being allowed to carry arms.
It's possible that George was used instead of Cornelius because Cornelius might have been thought an Irish name. There was unrest in Ireland, rebellions in 1798, aided by a French invasion and another attempted rising in 1803. More unrest in early decades of 19thC.
What is evidence that Cornelius Senior was Anglican? If it's only that his name appeared in Anglican registers, that doesn't mean that he wasn't R.C. Marriages after Hardwicke's' Marriage Act (1750s) had to be in C. of E. The churchyard was the only place most people in the parish could be buried. Births & baptisms of Catholics were recorded in C. of E. register. Some Anglican curates included a note that the person was Catholic, some didn't. Some curates were meticulous, some were inconsistent.
Was Cornelius Senior alive at the time of the 1767 Return of Papists?
Some Catholics fluctuated in their adherence to one or other denomination depending on many factors. Some outwardly conformed to C. of E. to avoid fines for non-attendance at church or extra taxes or so that they could inherit or pass on property or have their sons educated or travel freely. Being Catholic at one time under penal laws was a bit like being under Covid-19 lockdown - not allowed to attend your church, not supposed to travel beyond a set distance without permission or a valid reason, not allowed to do certain jobs, not supposed to celebrate a wedding or funeral as you would prefer, not allowed to travel abroad without risking serious consequences on return.
Was the landlord or lord of the manor R.C. or C. of E.?