Final answer:
John and Abigail Adams were engaged in various diplomatic roles, especially during John's presidency when he managed the crisis with France, including the XYZ Affair and the Quasi-War. Abigail supported John through her letters and managed the homestead in his absence.
Step-by-step explanation:
Between 1783 and 1778, Abigail and John Adams were engaged in numerous diplomatic activities. However, this timeframe appears to be incorrect as the years are in reverse chronological order. Assuming the intended period is during John Adams's time in public service, it can be clarified that John and Abigail Adams did not open a restaurant or write books together, nor did they strictly stay at home during significant periods.
John Adams, who would later become the second president of the United States, was active in diplomatic missions, particularly during his presidency. He faced a growing crisis with France, notably the XYZ Affair and the subsequent Quasi-War, which led him to manage intricate foreign policy challenges and steer the nation through turbulent times. Throughout, Abigail Adams provided support through her correspondence with her husband and managed the family home while he was engaged in diplomatic efforts. Abigail's letters to John are noteworthy for their eloquence and historical significance.
Thus, the most accurate answer from the options provided would be that they went on numerous diplomatic missions.