There are several newspaper and magazine articles that mention Richard Child Willis. Many of them are riddled with inaccuracies. The article below is from the British Medical Journal, 11 January 1896, page 128, and the errors are pointed out in red. Some of the errors in here seem to have propagated into later articles.
DR. C.M. JESSOP (Redhill) writes: Can you tell me the Christian names of Dr. Willis and his son? A Dr. Willis was present when George III died, January 29th, 1820. The son built Raven Hall, near Robin Hood's Bay, and as natural shrubs and trees would not grow owing to exposure to the sea air, he planted iron ones, which were seen and heard jingling in August 1837, by a friend who inquires. The younger man was in the Church: one day he divested himself of his coat and vest and preached in Whitby parish church, year unknown. When and where did they die? The junior man was a hypnologist, and charged one guinea as a fee for procuring sleep at any time. [I don't know if this is correct or not!.]
Francis Willis, son of John of Lincoln (city). Cler. Lincoln College, Oxford, matriculated May 30th, 1734, aged 15; B.A. from St. Alban Hall, March 21st 1738-9; M.A. from Brasenose College, February 10th, 1740-1; B. and D. Med., 1759. He was rector of St. John's, Wapping, and Vicar of Ashby-de-la-Laund, co. Lincoln. He was called in to treat George III at the suggestion of Dr. Addington. Some interesting deails of Dr. Willis's treatment are given in the third volume of Sir N.W. Wraxall's Posthumous Memoirs. Dr. Willis appears to have acted very disingenuously in his treatment of the King, but he received an annuity of £1,500 for twenty-one years, whilst to his son who had assisted him was awarded £650 per annum during his life, to which were added 30 guineas for each visit to Windsor, and 10 guineas for each visit to Kew. The elder Dr. Willis was afterwards sent for to attend the Queen of Portugal, whose religious mania he completely cured [No he didn't. He declared her incurable.] , a service for which he received £20,000. He established a private asylum at Greatford, co. Lincoln, where he died December 5th, 1807. He enjoyed a hearty old age, however, for when he was 72 he rode on horseback in one day a distance of 115 miles to attend his relative, Sir Charles Bourse, Bart. at Oxford. The son [grandson] of Francis Willis (Thomas? [No, Richard]) purchased Raven Hall about 1826 [inherited it in 1829] ; it was built by Captain Child in 1774, and added to the buildings forming the grounds and terraces. He got into monetary difficulties arising, it is said, from losses at Doncaster; and Mr Hammond, the late owner, obtained Raven Hall by foreclosure of mortgage. The Hall was offered for sale on August 9th, 1895. This Dr. Willis preached in St. Mary's Church, Whitby, about 1833 or 1834, after removing his coat and vest. There are at least two credible witnesses, now living in the immediate neighbourhood of Whitby, who testify that in August, 1837, they themselved heard that jingling of the iron leaves planted by Dr. Willis on the west side of Raven Hall, to which Dr. Jessop alludes. When he was in low water Dr. Willis advertised a system of obtaining sleep [See the comment in the question above] , but he charged a guinea for the prescription. The following has been handed down by a relative of the writer, who parted with his money: "The person to stretch himself out full length in bed, the arms being placed behind his back so that the chest may be enlarged. Then draw in the breath, at the same time dismissing every thought out of the mind, allow the same to escape gradually, and sleep will follow." He appears to have been a member of Caius College, Cambridge, but this statement requires verification. [It's wrong]