There’s no way to force IE to open Chrome unfortunately – allowing websites to open other programs would be a security risk.
Do you know which compatibility mode IE is set to? I think there’s IE 7, 8, 9 and 10 modes. It is possible to make IE turn off compatibility mode by adding a line of “code” to the output files – but this isn’t really practical as it would have to be added to a lot of files every time you published.
Another option could be to display a warning on your LMS asking people to move to Chrome if they’re using IE. How you would go about doing that depends on what LMS you’re using – you’re best asking your provider.