As the title says...
This only happens when I try to play LittleBigPlanet Vita or Need for Speed Most Wanted's online multiplayer modes. It will seemingly connect for a few seconds and in no time at all, my wireless router screws up and I'm unable to access the internet, requiring me to reset it to get it back to working order. As a result, I'm unable to play any sort of multiplayer against others in these titles.
Is there any way to fix this? I've even tried opening ports and using DMZ to no avail.
It is definitely a problem with your router. No device on the wireless network should be able to crash the router, even on purpose, much less by accident. Update the firmware on your router to the latest version. That usually solves the problem. If that doesn't work, then you will need to buy a better wireless router.