You can simply inject a copy of the element into each form right before submission.
This way, you can have the option of having different information for each hidden form field without affecting the other.
Something like this:
<script type="text/javascript">
$(function() {
$('form').submit(function() {
$("#hidden_element").clone().appendTo(this);
});
});
</script>
If you want to use the exact same element for both forms without creating a fresh copy, just don't use clone()
See documentation for clone() and for appendTo()
EDIT:
If you don't want to send the hidden element with every request the form sends. Consider storing it in the database for that user for that time. You can submit its content once, and once only for every page reload, and then just send the database id of the hidden element with each form post.
On page load, something like this:
$.post("page.php", { reallyBigObject : $("#hiddenfield").val() }, function(insertedID){
$("#hiddenfield").val(insertedID);
});
Then, in the server side code:
//insert $_POST["reallyBigObject"] into databse
//get the just inserted id (in php it's done with mysql_insert_id())
//echo, or print the just inserted id, and exit
This way your js gets the callback.
Now, you can submit the form as you would, but this time, you're only sending the id (integer number) to the server.
You can then simply delete the object from your server (run a cron to do it after X amount of time, or send another request to delete it.
Honestly, though, unless you object is HUGE(!!), I think storing it by submitting it only once is a lot more complex to execute than to simply send two requests to the server.
Let me know if you have any other questions...