Sorry to hear you are having difficulty with the update. A few things…
Do you have a Suitcase Fusion v18.1.0.pkg file in your downloads folder? This is what should be extracting from the .zip file you receive from the application update. If so, you can try right clicking and Open With > Installer.
If you are not seeing that file, you can download the installer directly here: http://bin.extensis.com/SuitcaseFusion7-M-18-1-0.zip and run the resulting .pkg file with the Installer.
Also, you might want to disable any anti-virus software you are running as that can sometimes interfere with the install process. Also any applications that are running at the time of install might be conflicting, so it is recommended to close those as well if you are having issues.