Perhaps the two most important textbooks you can own, for yourself and your children are:
1. For American History: The Growth of the American Republic, by Samuel Eliot Morison, Henry Steele Commager and William S. Leuchtenberg. Most recent edition 1980, earlier editions back to about 1950, earliest editions are just Morison and Commager. All distinguished historians trained before or just after WWII. New Deal liberals, more or less, of the New England and patriotic variety. Solid mainstream interpretations, if very much "Plymouth Rock" school. You won't get anything better, or nearly as good, in two volumes.
2. For European History: The Making of the Modern World World, by R.R. Palmer, Joel Colton & Lloyd Kramer. Most recent edition 2002, editions back to about 1950. Pre-1970 editions are Palmer alone. Kramer is new with 8th or 9th ed. This is generally considered the best text for a traditional freshman "western civilization" course as taught from the 1920's through the 1980's. Lucidly written and penetrating, it was also used as late as the 1970's by graduate students in European history as the last thing to read before taking exams, to pull all the specialized work together. Nothing better around. Palmer is a distinguished historian of the French revolution and the period preceeding it, and wrote a remarkable book of transatlantic history, The Age of the Democratic Revolution.