Complications of delaying divorce

My divorce becomes final on May 14th.  It should have happened a few years ago, but nothing can change what's done; it's simply important that we move forward.   However, I would like to point out one complication that may arise from delaying a divorce too long.   Reasons exist, and I don't want to go into them; the important thing to learn from my experience is whatever you do, don't delay.  Get it done.

After we decided to break up, my ex-wife ended up getting together with another man.  She had two sons by him.  Because the way states write family law, courts tend to consider them a "product of the marriage", even though there's no way I could have fathered them, and their mother freely admits they're not mine.  The separation agreement says they aren't mine, and my ex is not asking for support for her sons.  However, the court is now asking for DNA evidence that the sons aren't mine.

Say what?

Let me repeat it, because it bears repeating: my ex is not asking for any support, and the separation agreement clearly states that the boys are not mine, but the court wants DNA evidence to prove it. 

So...who pays for the test?  It's going to be up to me.  I had no part in the production or the raising of these children, and they live with their mother and father, but I am going to have to pay for a DNA test to prove the boys aren't mine.  

What's the reasoning here?  It makes no sense to me.  

In any case, I'm doing it and getting it over with so we can follow through with the dissolution on May 14th, but the idea of it has me boiling.  

If I had my head together when she asked for the divorce, I could have ended things with my ex in court before she had the first boy, so heed my advice: do whatever you have to do to make your divorce happen quickly.  Don't get caught up in "product of the marriage" nonsense--you could actually get stuck paying for support for children who aren't yours.  Ohio seems to care about paternity, but not all states are the same--some will not care who the father is, as long as the husband has an income.