Princess Augusta (1737-1813) was always styled 'Lady Augusta' during her father's life, but I've no idea why. Her birth was traumatic. Her father, the Prince of Wales, was determined to spite his parents no matter what, and resented their wish that the birth take place with them in Hampton Court. So when his wife went into labour, he had her taken half way across the city screaming in agony to St James's where Augusta was born. Her godparents were George II, Queen Caroline and the Princess of Wales's mother, the Dowager Duchess of Saxe-Gotha.
Princess Elizabeth's (1740-1759) godparents were the Margrave of Brandenburg-Ansbach, Queen Sophia Magdalena of Denmark and the Duchess of Saxe-Gotha (the sister-in-law of the Princess of Wales).
Princess Louisa's (1759-1768) godparents were Prince Frederick of Hesse-Kassel, Queen Louisa of Denmark (her aunt) and the Princess of Orange (her aunt Anne, nee the Princess Royal).
Princess Caroline Matilda's (1751-1775) godparents were Prince George (later George III, her eldest brother), Princess Caroline (her aunt, George II's daughter) and Princess Augusta (her eldest sister).
1.Augusta (1737-1813) m. Karl II (Wilhelm Ferdinand?) of Brauschweig-Wolf.
Not unlike her daughter Caroline in personality, she was mischeivous and told stories of sharing a bed with her brother George III when they were children, and claiming he wet the bed. The family constantly suspected her marriage was unhappy, but she never made any complaints about it. She fled to England during the Napoleonic Wars, and was reunited with her brother George after 36 years. She was the only one of his siblings to achieve anything approaching his great age.
Carolina Mathilde (1751-1775) m. King Christian VII of Denmark
Usually called Caroline Matilda, she was her father's posthumous child. Her marriage to her cousin (his mother was Louisa, George II's daughter) was a disaster, as is well known. It is widely believed that her second child, Luise, was fathered not by her husband but by her lover, Count Streunsee. She died in exile in Germany after the failure of her marriage.