Thanks for the clarification. If the first code you have added in the child theme already removes the website URL field but the placement of the submit button should be changed, then you can stick this the PHP code you had in the beginning and you could add custom CSS to move the button.
The name and the email fields have the default width of 33.33333% and are floated to the left that is why the button goes adjacent to it when the URL field is removed. To solve this, you can simply increase the width of the name and the email field to 50% so that the two fields will fill the entire block and the button will be displayed in a new row. The CSS selectors that controls the name and the email are:
Hope this will get you started.