Magpie, my daughter and I play the same way you do with your mom (although she's a room away). We play at the same time often, one of us online with Origin and the other staying offline. I also have TS4 on a laptop that gets used frequently. All three computers updated without problem, so I doubt Tixxis' suggestion would be the issue unless they were both trying to update at the same time.
However, Sanshifter could go to the computer that is updated properly and force Origin to log out (I'd reboot or leave it off after logging out), and then try again on the the one misbehaving. Maybe that would force it to recognize that there's no other game running. I'd also try repairing the game through Origin. I'm afraid I don't have another suggestion though except to contact Origin and see if they can force the update through anyway (no clue if they can).