I wrote the problem in StackOverflow at:
https://stackoverflow.com/questions/42538839/how-do-i-click-on-a-row-in-a-jquery-datatable-using-htmlunit

I have a unit test that can be used which directly accesses my website with an example web page. That source code is below.

(import java.io.IOException;
import java.util.List;

import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;

import com.gargoylesoftware.htmlunit.WebClient;
import com.gargoylesoftware.htmlunit.html.DomElement;
import com.gargoylesoftware.htmlunit.html.HtmlDivision;
import com.gargoylesoftware.htmlunit.html.HtmlElement;
import com.gargoylesoftware.htmlunit.html.HtmlPage;
import com.gargoylesoftware.htmlunit.html.HtmlSpan;
import com.gargoylesoftware.htmlunit.html.HtmlTable;
import com.gargoylesoftware.htmlunit.html.HtmlTableBody;
import com.gargoylesoftware.htmlunit.html.HtmlTableRow;


/**
 * @author gary_kephart
 *
 */
public class DataTablesTestCase
{
  private static final long   BG_JS_WAIT_MS = 15000;
  private static final String TEST_PAGE_URL = "http://photeus.com/campaigner-data/";
  private WebClient           webClient;


  public HtmlPage getPage(
    String url) throws Exception
  {
    HtmlPage htmlPage = this.webClient.getPage(url);

    this.webClient.waitForBackgroundJavaScriptStartingBefore(BG_JS_WAIT_MS);

    return htmlPage;
  }


  /**
   * @param domElement
   * @return
   * @throws IOException 
   */
  public HtmlPage clickOn(
    DomElement domElement) throws IOException
  {
    HtmlPage htmlPage = domElement.click();

    htmlPage.getWebClient().waitForBackgroundJavaScript(BG_JS_WAIT_MS);

    return htmlPage;
  }


  @SuppressWarnings("unchecked")
  protected <E extends HtmlElement> E getElementById(
    HtmlElement parent,
    String tagName,
    String id)
  {
    return (E)parent.getElementsByAttribute(tagName, "id", id).get(0);
  }
)

  @Before
  public void setUp()
  {
    this.webClient = new WebClient();

    this.webClient.getOptions().setCssEnabled(true);
    this.webClient.getOptions().setJavaScriptEnabled(true);
    this.webClient.getOptions().setTimeout(0);
    this.webClient.getOptions().setUseInsecureSSL(true);
  }


  @Test
  public void testSuccess() throws Exception
  {
    HtmlPage htmlPage = getPage(TEST_PAGE_URL);

    Assert.assertEquals("Campaigner Data - Home", htmlPage.getTitleText());

    HtmlDivision div = getElementById(htmlPage.getBody(), HtmlDivision.TAG_NAME,
      "elections_wrapper");
    HtmlTable table = getElementById(div, HtmlTable.TAG_NAME, "elections");
    List<HtmlTableBody> bodies = table.getBodies();
    HtmlTableBody body = bodies.get(0);
    List<HtmlTableRow> bodyRows = body.getRows();
    HtmlTableRow tableRow = bodyRows.get(0);
    HtmlPage htmlPage2 = clickOn(tableRow);

    Assert.assertEquals("Campaigner Data - HtmlUnit Datatable Row Test", htmlPage2.getTitleText());
    
    HtmlSpan elementIdSpan = getElementById(htmlPage2.getBody(), HtmlSpan.TAG_NAME, "elementId");
    String elementId = elementIdSpan.asText();
    
    Assert.assertNotNull(elementIdSpan);
    Assert.assertNotNull(elementId);
  }
}