Hi Clive. I realise this is a long time after you started researching your grandmother's history. I have just started however, and I have an Eveling Family tree, I think we are related.
Louisa, Derick and James are brothers and sisters of John, who is my Great great grandfather. One of his sons, Alfred James, married Cecily Harriet Pett, who had 11 children, 4 of whom died at a young age, 7 survived, one being my grandad, Ernest. They had one child, Mavis, my mum. And here I am.
I have another spelling for your Grandmother's father, Diederich. Apprently was born in Hanover, Germany, but moved to Spitalfields, London.
I'd be really interested to hear from you if you are still researching the family. My mum was once told by her Uncle Frank, that anyone found in this country who spells the surname the same, Eveling, will be a relation. I don't know how true this is, but it seems fairly true in this case.
Hope to hear from you.
Nicki Woodham