Teaching a class because advisor bought out and advisor input
In the long term, how much control should my advisor have over my class


None, for the duration of this instance. The advisor bought out. You're in charge. End of story. Now you might need some help in standing up to your advisor, and you need to bring in the chair of the department (who's already shown a willingness to help) and/or other senior faculty who manage curriculum activities. Don't do it confrontationally: merely say that you're really uncomfortable expanding the class size and don't feel like it's right to selectively admit students who have access to your advisor, but that you'd feel more comfortable with a faculty intermediary to help mediate. 


  In the short term, should I admit this waitlisted student?


No. you're right that this is both setting a bad precedent as well as being unfair. Again, as for how to proceed, see above. You haven't indicated exactly how the advisor is pressuring you, but I think it's fair to point out to them that this undermines your authority as the teacher, and you really need to maintain your independence because you're "only a student". Anyone with teaching experience should understand the importance of establishing authority and presence in the classroom.