You could automatically post the second form using JavaScript:

<script>document.forms[0].submit()</script>

This is the simplest method I can think of but I'm not an expert web guy ;)

You should also keep your current button and wrap a <noscript> around it for users with JavaScript disabled.

Edit: if you are using JQuery, Wookai's answer would be a better solution. But keep the noscript button.