Passing Session securely to shared ssl domain

[HairBomb]

Here is my situation, I have an e-commerce site www.mydomain.com and my host only supports shared ssl certificates, they do not allow private ssl certificates.  In order to easily keep the php session going for the shopping cart on the secure server which is https://mydomain.hostdomain.com, I am redirecting www.mydomain.com to http://mydomain.hostdomain.com as my sites address, which works fine. 

 

My first question is will any search engines have an issue with indexing or ranking a site address of mydomain.hostdomain.com? 

 

I would however like to use my actual domain for my site because it would look more professional to customers, but what is the best way to do that?  I know I could use www.mydomain.com and pass the session id through a url to the secure server and recreate the session there, but I'm wondering if that creates too much of a security risk and if not, what is the best way to do it securely?