[ubuntu] GRUB and FullDiskEncryption

Hello, I am Lorenzo. I am a new forum user, but I am not new to the world of Ubuntu: I have been using it for years. I have always been able to solve my issues discussing with the friends of the Italian Ubuntu forum, but during the last week I installed Ubuntu 12.10 using the Full Disk Encryption and I encountered a problem that we was not able to solve. So I registered to this international forum, hoping to find some Ubuntu-Pro who would like to assist me.

Here is the problem:
I have to use Ubuntu in a computer which is used also by my parents, and they does not permit me to install GRUB, since it is loaded every time they start the PC. So I decided to install Ubuntu without any boot loader, and then to install GRUB on a USB flash drive. My idea was to simply boot from the USB and to load Ubuntu whenever I wanted to use it. :)
I installed Ubuntu manually using FDE (without any boot loader), and then, from the live CD, I created a bootable USB flash drive through the procedure that is used for creating USB sticks for installing ubuntu (e.g. for computers without CD drive). When I boot from the USB GRUB starts, but I do not see any partition and I am not able to run Ubuntu (the only possibility is to start the live version of Ubuntu contained in the USB device).

The partition scheme of my PC:
sda1: windows 7
sdb1: boot partition created during the manual installation of Ubuntu (300MB)
sdb2: NTFS used for data storage
sdb3: Ubuntu installed using FullDiskEncryption

I think that I should indicate to GRUB the location of the partition containing Ubuntu, but I don't know how, and I don't even know which is the correct partition (boot or the one whith FDE).
Every advice is welcomed, thank you in advance.

Lorenzo