Ex Wants to Reduce Support, I'm Not Going

My question involves child support in the State of: Michigan

Ok, so the ex wants to reduce her child support to me. She is supposed to pay 400$month. We have 2 kids, and they live with me 6 days/week.
She is a nurse, though unemployed, and has been for some time. She has the ability to make about 25$/hour. The 400 month was something that we agreed to in our divorce judgement, it would have been much higher, but all I asked for was that she pay for daycare while I worked, which, in fact, has now gone up to 600/month.

She claims she is unable to find a job, which is total crap. I am a nurse as well, and to prove a point I put out 3 applications last week, and within a couple days I had 2 call backs and interviews scheduled.
She is also able to pay her car payment, and recently purchased an Iphone. She is about 6 months in arrears right now.

So I am not planning on going to the hearing. Why? Because I will lose 200 plus daycare if I don't go to work. Because even if they don't change the order, she still won't pay it. Because I partly feel that if she doesn't want to support her children, that's her problem, it's on her.

If I don't go, will it pretty much guarantee they will reduce her support?

Unfortunately yes - if you don't respond, she'll likely get what she wants.

would it do any good if I wrote a letter and delivered to the friend of the court, outlining why I don't think support should be reduced?

You need to actually respond to the motion.