Jacques,
Did you read the Stack Overflow page I linked to? It does not mention Protected Mode at all and clearly indicates that this is an issue with how IE deals with security inside of an iFrame (and it's a
widely known issue). If other browsers deal with it differently it's partly because of a different philosophy; remember that IE is widely used in governmental and financial institutions, so security has to be treated differently in that regards. Chrome, FireFox and Safari are catered towards end-users, for which it's more important to have function than security (up to a certain extent).
Again, what you're trying to do is and unsupported method of doing "integration", which is slapping a website inside an iFrame and hoping it will work. You need to use the methods described in the Web Integration guide if you wish to have a fully functional implementation. Anything else is patching and hacking and leaves the door open to much issues in the future, whether technical, security or legal.
Finally, I'll re-instate the point we've been trying to make about support: You can use our mutual client's credentials (serial number) in order to receive support, with their permission.