Others here on Moodle.org should have some ideas for you. I don't do what you want to do, so I am only providing an idea.
In your Moodle course, you might be able to have the very top item be a "quiz" that has only one question in it, a True/False question. The question is "You can attend all dates?" The correct answer is "True." Then, every other activity in your Moodle is "conditionally" linked to the student "passing" this quiz. You should be able to use "Activity Completion" and/or "Restrict Access" to do this. I don't use these features in my courses, so I am only trying to guide you.
To automatically "remove" a student, you would need some kind of SQL
query that looks at the student's "grade" on this quiz, and if it is not 100%, changes their status in the course to "suspended." I tend to prefer "suspending" students to removing them. This way, you retain a record of all students who entered this course. But you have to think this through on your own.
As another alternative, why don't you simply email the students the date, and ask them if they can attend. If they can, you give them a self-enrollment password (key.)