This Google Apps Script sorts two columns. Variables can be modified to define what two columns should be sorted, and whether they should be ascending or descending.

GA-sort-two-columns.js

/** Build a menu item
From https://developers.google.com/apps-script/guides/menus#menus_for_add-ons_in_google_docs_or_sheets 
**/

function onOpen(e) {
  var menu = SpreadsheetApp.getUi().createMenu('Sort'); 
if (e && e.authMode == ScriptApp.AuthMode.NONE) {
    // Add a normal menu item (works in all authorization modes).
        menu.addItem('Sort Sheet', 'sort');
  } else {
    // Add a menu item based on properties (doesn't work in AuthMode.NONE).
    var properties = PropertiesService.getDocumentProperties();
    var workflowStarted = properties.getProperty('workflowStarted');
    if (workflowStarted) {
          menu.addItem('Sort Sheet', 'sort');
    } else {
          menu.addItem('Sort Sheet', 'sort');
  }
   menu.addToUi();
  }
}

function sort() {
  
  /**  Variables for customization:
  
  Each column to sort takes two variables: 
      1) the column index (i.e. column A has a colum index of 1
      2) Sort Asecnding -- default is to sort ascending. Set to false to sort descending
  
  **/

  //Variable for column to sort first
  
  var sortFirst = 2; //index of column to be sorted by; 1 = column A, 2 = column B, etc.
  var sortFirstAsc = true; //Set to false to sort descending
  
  //Variables for column to sort second
 
  var sortSecond = 3;
  var sortSecondAsc = false;
  
  //Number of header rows
  
  var headerRows = 1; 

  /** End Variables for customization**/
  
  /** Begin sorting function **/

  var activeSheet = SpreadsheetApp.getActiveSheet();
  var sheetName = activeSheet.getSheetName(); //name of sheet to be sorted
  var sheet = SpreadsheetApp.getActive().getSheetByName(sheetName);
  var range = sheet.getRange(headerRows+1, 1, sheet.getMaxRows()-headerRows, sheet.getLastColumn());
  range.sort([{column: sortFirst, ascending: sortFirstAsc}, {column: sortSecond, ascending: sortSecondAsc}]);
}

Works perfect for us. Thanks so much!

Works great for a single sheet, but is there a way to have it run for all the sheets in the file? Or, ideally, all but the first one?

@Kwikiwi

To run through all the sheets in a file, I'd try something like this:

var ss = SpreadsheetApp.getActiveSpreadsheet(); 
var sheets = [Insert sheet names here ex. 'Main', 'Detail', etc.];  
for (var i = 0; i < sheets.length; i++){  
  var s = ss.getSheetByName(i);  
  Insert sort or whatever else you need here and it will loop through each sheet specified in the array 'sheets'  
}

On google script, it doesn't sort automatically after you type. You need to manually run the sort function just to sort it.