Trying to add menu items to a menu programmatically

A client’s site is having a problem and I spent several hours trying to fix it, but they want their updates “done now” so I added the posts with the “insert post” function and that all went swimmingly… but when I tried to update the nav, I successfully created nav items, but i have no idea how to assign them to a specific menu. I have the menu ID, I have the page ID’s… I need to add a “parent” item and two sub-menu items to the third (out of 4) position on a specific menu.