Hi,
What I see is that, when a product is removed from the cart, the user is redirected to the HTTP version of the website when previously on HTTPS.
By changing the domain, I think that the session is lost or is destroyed. That's why the user is logout after that.
Please check your joomla configuration, specially for the default url of the website. If "http" is mentioned in the configuration, it would explain why HikaShop make a redirection to an HTTP url.
Best 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.