.adminform button, #adminForm button, .button, button, a.readon, .pagenav-next a, .pagenav-prev a, input[type="submit"], input[type="button"], span.addtocart-button input.addtocart-button, .show_cart a, div.mobileSwitch > a {
  background: url("../images/style1/btn.png") repeat-x scroll 0 bottom transparent;
  border: 1px solid #D1D1D1;
  color: #383838;
  display: block;
  float: left;
  font-family: Arial,Verdana,sans-serif;
  font-size: 11px;
  font-weight: bold;
  height: 22px !important;
  line-height: 26px;
  margin: 0;
  padding: 0 8px;
}
 

 
span.quantity-controls input.quantity-plus,
span.quantity-controls input.quantity-minus  {
  height: 16px !important;
}

Through here: VM Backend > Configuration > Checkout

If you disable this On checkout, ask for registration option
Then the "the login / register div" will be gone in the shopping cart. This is normal. Not recommended but some people want to disable this. Its their call.

So what i did in your website:

1- browsed your website,
2- Add product to shopping cart
4- Only "checkout now" button was available at the bottom to proceed (which is normal)
5- I clicked that button and it gave me a form to fill out.
6- i filled out that form, and got this error: "Si prega di registrarsi per procedere con l'acquisto"

Which i believe means; "you need to register."

So in the VM Backend, disable this option:
Through here: VM Backend > Configuration > Checkout

Only registered users can checkout

So virtuemart will let users to finish the order without being registered user, then let me know. I will re-test your website to see what is going to happen when i try to place 2nd order.