How to put a custom form inside node form with own submit button?
you should use an ajax in inner form on submit like :

  $form['activity']['submit'] = array(
  '#type' =&gt; 'button',
  '#value' =&gt; t('Execute'),
  '#name' =&gt; 'test_button',
  '#ajax' =&gt; array(
    'callback' =&gt; '_handle_form_submit',
    'effect' =&gt; 'fade',
),
);

 function _handle_form_submit($form, $form_state) {
 // your stuff here
 }


you can see ajax example modules Ajax Examples