Evict a tenant with late rent, and addendum violation

[Justin Poust]

I currently have a tenant that hasn't paid since April.  We came to an agreement that we would amend the lease and use her security deposit to cover May's rent, if she agreed to leave 6 June (lease was through Oct).  She has not paid for June rent, May's rent fee or left the premises as the Addendum annotates.  We went to small claims court today and the Judge didn't seem to care about the June 6th date on the addendum or the other lease violations that needed fixed per the addendum.  The judge only focused on Junes past due rent, said we didn't give a Notice to Quit for that (we did in May, but part of the agreement was to not file for early move out).  Does anyone have experience with a Addendum and it's validity?  How should I proceed?