How to subclass a parent for mocking

How do I subclass a parent class with a private constructor so that I can mock it?

I have refactored my code such that when it makes a call to a third party library, the calls are wrapped so that I can mock the class and create a fake wrapper. I can then in theory return whatever I want to test my production code using dependency injection etc.

For a few of the library calls, a single object instance is returned which in itself is a specific library object type. In the production code, this then has subsequent calls made upon that object.

This is illustrated in the code below:

public class MyWrapper
{
  public LibraryObject getX()
  {
    LibraryObject x = ExternalLibrary.getX();
    return x;
  }
}

public class MyProductionCode
{
  public void DoX()
  {
    LibraryObject lo = MyWrapper.getX();
    ProductionType pt = lo.doSomething();
  }
}

How do I fake the method doSomething() ? My first thought was instead of returning an instance object from the wrapped call, return an object which is of the same type. So MyWrapper code could be enhanced as follows:

public class MyWrapper
{
  public LibraryObject MyWrappedCall()
  {
    //LibraryObject x = ExternalLibrary.getLibObject();
    MyMockLibraryObject mlo;
    return mlo;
  }

  public class MyMockLibraryObject extends LibraryObject
  {
    public ProductionType doSomething()
    {
      ProductionType pt;
      return pt;
    }
  }
}

The problem with this is that the parent class has a private constructor, so it cannot be subclassed.

Does anybody have any suggestions of how to get around this?