What I would do is look up jobs that will offer an actual paycheck. The court will be more likely to offer emancipation when it can be proved that you're capable of living completely on your own.
You'll also need to keep your grades up and have a transcript of your school grades for the court.
While looking up a job, keep tabs on and record when your mother goes out, for how long and on what days-as well as her physical condition when she arrives home. It's all well and good for a single mom to have a relationship, but if she's focusing more on the relationship than your well being.
If you could give me the Boyfriend's full name, I may be able to do a background check on him.