You're not going to be able to see the web  part contents in a standard mobile  view. The mobile view displays list item content  and the web part content is separate from that, and I'm not aware of any way to include that content in the mobile view.

To approach this sort of problem you need to try something a little more complicated like this;
You have control over the way the web part renders markup (assuming you wrote it) so it can be made to render mobile friendly markup. In addition, you can re-write the Sharepoint page itself to be XHTML compliant by overriding the page Render method and manipulating the markup before it's sent to the browser. XHTML compliant markup is good enough to be viewed in all modern mobile devices (you don't need to worry about WAP anymore unless your client says otherwise!). The markup you intercept from Page Render will have the content from the page and from any web parts. That's how you can display it in a mobile device.