Hi,
If you're using the same server, with the same Joomla/HikaShop (so the same database), you will need to have a shared session.
So the users will have the same session in the two domains ; thanks to that, they will keep their cart (their login, etc) in the two domains.
I don't see that your solution will work. This is session cookie and it will changed its key for different users as far as I know. Try with different browsers, or with the private mode of your browser.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.