You should be having no issues with sending videos in a group message on the note 2. I have it and never had that issue. What version of android are you running? I send videos and pictures all the time to multiple people. Let me know if you need help.
Sure..my note had 4.1.2 when i had it.. I would like to use the camera app to take a good quality 1 minute video and send an mms via the stock sms app without the video looking like a pixelated piece of....