You will find the legal case in the "Law times reports", Published by Law Times Office, 1861 (v. 4).
Also Thomas Mitchell Shadwell's Book on Charles Fearne on
Try a search for "Thomas Mitchell" and "Shadwell"
I have found several references which show Dr John Shadwell (born ca. 1762) and Thomas Mitchell Shadwell as being the sons of John Shadwell of the Inner Temple, Barrister at law, by his wife Isabella Mitchell daughter of Thomas Mitchell of Mitchellsfort, co. Cork.I have been working on this Mitchellsfort family (although have no apparent connection).The elder John Shadwell's will is in the Bristol Archives.
Please contact me directly for further information.