My father, who was the son of a priest, pointed out that the only reasons, he knows, a second baptism/christening can occur are the following:
1. The vicar is de-frocked!!!
2. Pauper's baptism then the real thing
3. Change of denomination!!!! Say catholic to methodist or protestant....
Normally you can only be baptised once in that denomination!!
I too have a double christening, but at different churches, St Botolph without Aldgate 11/4/1827 and St Olave, Hart Street 4/3/1833, both given with the same name, parents and birth date!
My entire family clan had moved from one church to the other (change of denomination?) and re-baptise a child already covered. I know that it must be the same child as she maintains her correct age all through her life and a sibling,
who is baptised at the same time, is staying with her in a much later census in 1871!

So.....it does happen!!!

Geoff.