As you all know, when you buy a Wii console, it automatically comes with one Wii Remote. That Wii Remote works fine. A little while ago, I got a second one which was a MadCatz version. For some reason, it only works in multiplayer.
In other words, if I'm playing New Super Mario Bros. Wii, I can only use the MadCatz Wii Remote if the original Wii Remote is already turned on (controlling Mario) with me then turning the MadCatz Wii Remote on in which it would be controlling Luigi. I can't seem to use the MadCatz Wii Remote to turn on the console either. 
When it comes to the MadCatz Wii Remote, how can you play in Single-Player mode without turning the original Wii Remote on first? The MadCatz Wii Remote is my mom's, by the way.

If any of you have been in this situation before or know how to fix this problem, please help!

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Press the home button, click wiimote settings, choose reconnect, press 1+2 on the madcatz remote. This makes the madcatz remote player 1.

I would also try resynchronizing the wiimote and console. Not sure where MadCatz puts the button, but on the standard wiimote there's a little red button under the battery cover. Push that button at the same time as the little red button next to the Wii's SD card slot and you'll associate the wiimote with the Wii.

Assuming you can do so... you need to properly sync the remote with the console (as ringo says)
If you have done that and it is still doing this then I don't think anyone here can help unless they had the same problem. But you should still be able to swap players as Pyro said (but the Wii has to be on already)

This is why I only buy 1st party products. They simply always work and if you search good enough you'll pay less or the same.

Next time buy one of the billion wii remotes from ebay for ~$20. That's how I have four.

I just tried that (after your comment) and it worked, but not permanently. I was able to turn the console off with the MadCatz Wii Remote, but as soon as I'd done that, the Wii Remotes automatically switched back and I was only able to turn it back on with the regular Wii Remote.

GameGuy,

Unfortunately since that remote is unlicensed, it can cause issues with other remotes that are synched up. I recommend you clear all syncs on the console and try again. Hold down the red button on the Wii while it's turned on for 10 seconds. After that, try to re-sync the remotes one at a time. If you're still having an issue, then you'll need to get rid of that Mad Catz remote and get an official Nintendo one.

I would suggest burning the MadCatz controller and buying a real Nintendo controller.

In my experience, a MadCatz controller will only last 2-3 weeks without even touching the thing. For the $5-10 you save, they die so much faster that it isn't really saving anything.

This is why I only bu.. err, own first party hardware. They usually work for far longer.

I hope things work out for you, though.