Problems with update / permissions

Do you have Administrator privileges?

Are you sure that your first account has Admin privileges?

I would log into the second account and then Repair Permissions.

Besides repairing permissions with disk utility, you need to reset your user permissions. Follow instructions here:

Repairing User Permissions in OS X Lion

You’ll need to reboot to perform this, and then use the same resetpassword utility that is used to change passwords in Lion, but instead choosing a hidden option.

When you use the Disk Utility app and Repair Permissions — it doesn’t actually repair the permission settings on folders and files in your Home folder where your documents and personal applications reside.

In Lion, there is an additional Repair Permissions application utility hidden away. This toolis located inside boot Repair Utilities. Here’s how to access it.

1. Restart Lion and hold down the Command and R keys.
2. You will boot into the Repair Utilities screen. On top, in the Menu Bar click the Utilities item then select Terminal.
3. In the Terminal window, type resetpassword and hit Return.
4. The Password reset utility launches, but you’re not going to reset the password. Instead, click on the icon for your Mac’s hard drive at the top. From the drop-down below it, select the user account where you are having issues.
5. At the bottom of the window, you’ll see an area labeled ‘Reset Home Directory Permissions and ACLs’. Click the Reset button there.

The reset process takes a couple of minutes. When it’s done, quit the programs you’ve opened and restart your Mac. Notice that ‘Spotlight’ starts re-indexing immediately.