Try using Revo Uninstaller. Even if it can't uninstall the application normally, it will force it to uninstall by wiping out all traces of its presence from the system.
After that, try running AdwCleaner to make sure that there are no leftover rogue registry keys or toolbars in your system.
Once the application is removed, right click the file you want to open and then select Open with. Choose the Adobe program you want and that's it. Now the files will be opened with Adobe.