If you're handling the form processing using JavaScript, then you'll want to return false in your button and form processing code.
I was able to achieve identical results using the JavaScript below, and the two HTML examples (with the button inside and outside of the form element).
JavaScript/jQuery
$("button").live('click', function() {
$("#checkin").submit();
return false;
});
$("#checkin").live('submit', function(){
alert("Hello world!");
return false;
});
HTML Example 1
Button inside the form.
<form id="checkin" name="checkin" id="checkin" action="" method="post">
<input type="text" tabindex="100" class="identifier" name="identifier" id="identifier">
<input type="submit" tabindex="101" value="Submito" class="elsubmito" name="submit">
<button>test</button>
</form>
HTML Example 2
Button outside the form.
<form id="checkin" name="checkin" id="checkin" action="" method="post">
<input type="text" tabindex="100" class="identifier" name="identifier" id="identifier">
<input type="submit" tabindex="101" value="Submito" class="elsubmito" name="submit">
</form>
<button>test</button>
As I said, both examples performed as expected. You may want to double-check your button listening code to ensure that you are in fact using the button element. If you're using an element with the id attribute set to button, then you'll want to ensure you are using the proper jQuery selector:
$("#button").live('click', function() { // ...