There aren't many programs that can edit m2ts files as it's a proprietry format that Sony keeps a tight grip on.
Sony Vegas and CyberLink can handle them, or you could use a converter to convert to a more common format before editing.
See
here for instructions and links.
CyberLink PowerDVD
CyberLink PowerDirector
Sony Vegas Movie Studio
Sony Vegas Pro
EDIT: A cheaper option might be to buy a new DVD drive that is definitely supported by ImageMixer 3. You'll have to check the manual or contact the supplier for a list of supported drives or confirmation that your new one will work.