That's weird man, because I've never had anything like that happen in HOI3 ever. In my Italy game, I managed to conquer Yugoslavia, Greece, Spain, Vichy France, Turkey, Iraq and Kick the United Kingdom out of Egypt, Judea, and Gibraltar, Malta, and Cyprus. Yes, I have remade Mare Nostrum. When the United States finally joined the Allies, their main route of attack, with the UK, was to make landings in Spain and Northern France, and the Netherlands.
Containing the landings has been hellishly difficult, but far from impossible. If you are prepared to deal with the United States, that is cut off any foothold in Europe that they gain, you're set and ready to go, no problem. The only way they're getting in is if you're caught unawares. Even if they do, if you cut off their access to ports, their armies will starve and will be easy pickings.
Say what you want about the supply system in HoI3 and how it ties your hands, but it does make things equally difficult on the AI. Once the States made a huge landing of thousands of infantry and several medium tank brigades in Gibraltar, and I was able to hold, and eventually defeat them with only 5 brigades of Paratroopers, because I was able to bomb the port in Gibraltar to hell, ensuring they could never resupply or reinforce the army.