Yes, it can be done, and quite easily at that. You do need to be able to modify your domain's host records, though. Simply create an A record for the subdomain store.domain.com and point it to the IP address of the second vps. Remember, you also need to create an account in the second VPS for store.domain.com. For your main site, create or change both the @ and www host names to an A record and point it to the IP address of your old VPS.
If you're not sure how to do that or don't have access to the host records, then contact your domain registrar so they can do it for you.
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