Hi tioljk,
" I have tried to update with multiple problems."
How did you upgrade your Window8 to Windows 8.1 ?
We can refer to the following link to upgrade the machine
Update to Windows 8.1 from Windows 8
http://windows.microsoft.com/en-hk/windows-8/update-from-windows-8-tutorial
We would appreciate it if you share us the exact issue you have come across and we will try our best to help you to resolve the issue .
"how can I keep it from trying to update to 8.1 and yet still get other critical updates."
What do you mean by saying this ?
If you want to downgrade the Windows 8.1 to Windows 8 , we can make it if we have got a Windows Recovery Disks .Here is a discussion about this operation for reference :
Windows 8.1 downgrade back to windows 8
http://www.eightforums.com/installation-setup/53806-windows-8-1-downgrade-back-windows-8-a.html
NOTE: This response contains a reference to a third party World Wide Web site. Microsoft is providing this information as a convenience to you. Microsoft does not control these sites and has not tested any software or information found on these sites.
Best regards