Hi EDO
It appears that my own grt grandmother Elizabeth Cottrell 1836-1907 may well have been your grt grandmother's second cousin.
Elizabeth's father was Charles Cottrell (architect) whose business address was Wandsworth Bridge, Cork City. In turn, Charles father was Francis Edward Cottrell, also an architect of the same address.
The reason that I feel that Francis the Architect and William the Attorney may have been brothers is in the registry of Deeds there is a lease dated 29th October 1804 concerning both Francis and William. I will have to get a copy to get the full details.
Even though I live near Cork, I have found it very difficult to find any information on this family and felt that they had all emigrated. There is another family of Cottrell's based around Baltimore in west Cork who are not related.