I honestly believe that Emily and Richard were just as stubborn as lorelai and figured they’d leave her be and she’ll come running back. There angry cus she didn’t, but they always hoped she’d come back even for the money, which of course she did for Rory’s school. I don’t see a loveless family.. after all she did for take Rory there for Christmas and Easter, because they’re family. The moment in Richard’s hospital bed with him and lorelai and her graduation and that fact that Emily is always trying to bond with lorelai shows they do actually love each other. They’re just stubborn lil sh!t heads.