Going after money from judgement in Michigan

[Rivy S.]

I had a tenant that missed rent for 2 months.  During eviction proceedings, we came up with a settlement that she would pay an extra 200/month until she is caught up.  At the time, I had a really lousy management company, who I fired soon after.  When switching over to a new management company, it took a few months to get the documentation from the old one about the money judgement.  This month they began charging her the extra 200/month (the outstanding balance is 1100).  When she saw the extra charge, she sent in 30 day notice that she's leaving, because it's too expensive --without paying this months rent! (lease was expired, she was going month to month)

So, I've got 2 questions: 

1. Is there any way/point in going after the 1850 (1100 +750) that she owes me? The property is in Michigan. 

2. If she's not going to be paying, do I really have to let her stay the rest of the 30 days?? It's probably not worth filing an eviction when she's leaving anyway, but it's upsetting to have to wait to do a turnover because a tenant who is not paying is living there!