It's probably not a bad idea to highlight the courses that you've taken even if you are also including transcripts. Depending on the employer, they may not necessarily look all that closely at your transcripts while sorting through the applicants. Also, you can use this as an opportunity to point out any specifics you may feel are relevant - a particularly interesting project, for example.
That said, a resume is all about presenting the most relevant information about yourself in a small space. I wouldn't cut out previous experience as a tutor to include specific course work.
As to whether the employer will request transcripts, some will and some won't. It depends on the position and whether they feel that a certain level of formal education is required. A tutoring group might, for example assess you through an interview or mock tutorial.