You might try limiting your allowed Shipping Destinations to at least eliminate the longest names, since that Ship to Country menu seems to be the main factor preventing your cart display from getting any narrower. You can go to Seller Admin > Cart Shipping Settings, select the Shipping Destinations you want (hold Ctrl on PC or Cmd on Mac to select more than one), click Next to apply changes, then Back to Admin.
Other than that, if you cannot widen the IFRAME and must display your shopping page inside that IFRAME, then the cart you are seeing is the best you can get since the cart must be trapped inside the confines of the IFRAME. There's no way technically possible to get the cart to pop out of the IFRAME unless you use the non-JavaScript version of our cart button codes that open the cart in a separate window/tab.
As to the third-party cookies issue, the main problem with that is that buyers who block third-party cookies will simply be unable to buy more than one item at a time, and may not even be able to do that much.