How to take contents of a tab and insert them inside a node
You can create a block using the block module hooks and you can generate the content of the block by using the page callback function in the menu to get the signatures displayed inside the block. You can then configure the block in whichever region you want.

Another option would be to use the page callback function inside the template file (.tpl file) of the petition  node and print the content near to the petition form.