Mario Kart WiiMix has been tested on NTSC Wii consoles and versions of the game only and should work fine outside of online play which will not properly work and time trials which you can do for fun, but does not save records.
I have not tested it on Wii U but it should work via that console's Wii channel.
A Wii set up with Homebrew.
A tutorial can be found here. Personally I used the LetterBomb exploit and it was very easy.
An SD card with sufficient space.
You should have already used one for setting up the Wii with Homebrew. You will need to use the same one.
The Riivolution app installed via the Homebrew Channel.
If you've installed a previous version of Mario Kart Wii Mix, delete the sqlmkw folder from the root of your SD card.
If you've installed a version of Mario Kart Wii Mix prior to 1.3, you will also want to delete any files starting with squadaloomkwii from your riivolution folder.
Unzip the files from the zip into the root of your SD card. This should create a riivolution folder if you don't already have one or if you already do, place an xml called "squadaloomkwii.xml" inside of that folder. It should also create folder called sqlmkw.
Insert your Mario Kart Wii disc then launch the Wii and navigate to the Riivolution Channel
In Riivolution Channel find the tab for Mario Kart Wii that says "Mario Kart WiiMix" or "Squadaloo" if using a version prior to 1.3.
Enable the "Enable Pack?" option. You can optionally also copy your vanilla game save file to SD card or replace Baby Daisy with Shy Guy.
Launch the game. You should be greeted with a new startup screen that replaces the old Wrist Strap warning screen if everything launched correctly.
Mario Kart WiiMix can easily be launched in the newest Dolphin Beta releases and the "Start with Riivolution Patches..." option, but it does require some additional minor setup for music to work properly.
The Latest Dolphin Beta or Development versions.
Do NOT use the stable release, it's 6 years old and lacks many modern features of Dolphin including the "Start with Riivolution Patches..." option.
A vanilla Mario Kart Wii iso file.
Nobody can legally provide this to you (at least in the United States). You must dump it yourself using your own copy of the game. If you've set your console up with Homebrew, it should be easy to do. Personally I used CleanRip.
The Track Music Expander Gecko code.
Grab the LE-Code version that matches your iso file's region.
If you haven't already, launch the Dolphin emulator and set up your game file directory to locate your Mario Kart Wii iso file.
If you've installed a previous version of Mario Kart Wii Mix, delete the sqlmkw folder from Dolphin Emulator's Load\Riivolution folder (The Dolphin Emulator folder is likely in your My Documents default location).
If you've installed a version of Mario Kart Wii Mix prior to 1.3, you will also want to delete any files starting with squadaloomkwii from your riivolution folder.
Unzip the files from the zip into your Dolphin Emulator's Load\Riivolution folder (The Dolphin Emulator folder is likely in your My Documents default location). This should create a riivolution folder if you don't already have one or if you already do, place an xml called "squadaloomkwii.xml" inside of that folder. It should also create folder called sqlmkw.
In the game list, right click on Mario Kart Wii and click on properties.
Click on Gecko Codes and add the Track Music Expander code via the "Add New Code" option. Make sure you add the version that matches your iso's region. Then, check the code to enable it.
Note that using this code without using an LE-Code distribution that supports it will cause the game to crash whenever a track loads. If you want to play the vanilla game, you will need to go into codes and disable this code before launching the game again.
Right click on Mario Kart Wii again in the Game list and this time click "Start with Riivolution patches..." You should see a new window with a box that has options for Mario Kart Wii Mix if everything was done correctly to this point.
Enable the "Enable pack?" option. You can optionally choose to replace Baby Daisy with Shy Guy (admittedly I don't know how the save to SD card option works on an emulator).
Note: I'm currently working on an app for Windows to just auto do some of this process, but for now here's the full thing.
Mario Kart WiiMix can be used in virtual reality with Dolphin VR, but unfortunately since Dolphin VR is based on an older version of Dolphin which lacks easy Riivolution support. You'll basically need to use a vanilla Mario Kart Wii iso file as the basis for creating a separate Mario Kart WiiMix iso.
A fully set up install of Dolphin VR. View the Dolphin VR settings page for more details.
A vanilla Mario Kart Wii iso file.
Nobody can legally provide this to you (at least in the United States). You must dump it yourself using your own copy of the game. If you've set your console up with Homebrew, it should be easy to do. Personally I used CleanRip.
The Track Music Expander Gecko code.
Grab the LE-Code version that matches your iso file's region.
A VR headset capable of connecting to PC, along with a PC capable of running VR games.
I've seen this asked in a couple spots, but to be extra clear: an Oculus Quest or Oculus Quest 2 will work for this ONLY if you use Oculus Link/Air Link/Virtual Desktop to connect them to a PC running the game. There is no Dolphin VR build that can run natively on a standalone VR headset as of this writing (July 2022).
This is a command line tool, but don't worry if you aren't comfortable using the command line, we'll only need it briefly twice.
Patience
This is a somewhat manual process and can be quite tedious if you haven't done modding before. Many of these steps can be avoided after your first time if you need to update your pack.
Note that this tutorial is written assuming you're using Windows (or specifically Windows 10). The steps involving the command line in particular may differ wildly depending on operating system.
If you haven't already, launch the Dolphin VR emulator and set up your game file directory to locate your Mario Kart Wii iso file. It shares settings with base Dolphin so you should not need to set this up if you've tried regular Dolphin before.
Use the Dolphin VR setup page and try running normal Mario Kart Wii first to ensure your setup is complete.
Navigate to the folder that has the Mario Kart Wii iso file in Windows Explorer (the standard file explorer). Ensure no folders are selected and click on "File" then "Open Windows Powershell. You should see a prompt with the path of the same folder you navigated to in explorer.
Type in or copy and paste the following command replacing MarioKartWii.iso with the name of your iso (right click is paste in Powershell): wit extract MarioKartWii.iso .\MKWiiMixVR
This will take a while to finish, you will know if it finished successfully once the command line cursor starts blinking again and there are no error messages.
Look back in Windows Explorer. There should now be a folder called MKWiiMixVR in the same folder as your original iso file. This contains an extracted version of all of the game's files.
Extract the Mario Kart WiiMix zip file.
Next, you'll need to copy a bunch of files from the sqlmkw folder you just extracted out of the zip into their proper locations in the Mario Kart Wii folder structure. Here's a table of file locations in the sqlmkw folder and where you copy them to from inside the MKWiiMixVR game folders.
Once you've copied all of the files, return to your powershell window and enter the following command: wit copy .\MKWiiMixVR MKWiiMixVR.iso
In Dolphin, add the new iso to the game list, then right click it and click on properties.
Click on Gecko Codes and add the Track Music Expander code via the "Add New Code" option. Make sure you add the version that matches your iso's region. Then, check the code to enable it.
Note that using this code without using an LE-Code distribution that supports it will cause the game to crash whenever a track loads. If you want to play the vanilla game, you will need to go into codes and disable this code before launching the game again.