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I applied to my dream school at an earlier cycle, but I am still on the waitlist. I just received an acceptance letter from another school with a $18000ish scholarship per year.

Does anyone have any idea about how to use my current admission and scholarship as leverage to argue with the school that waitlists me?

I don't think you can use a scholarship offer at one school to urge another school that has waitlisted you to accept you. Admitted students can negotiate scholarships, but un-admitted students can't really negotiate anything. You don't have leverage before you're admitted. Just keep emailing the school that waitlisted you to apprise them of any developments in your professional or academic life and to reiterate your interest in attending the school if accepted.