Hello,
normally it shouldn't be a problem to install Adobe's products on a second ( I use this term here too) computer. But it could be a problem of activate/deactivate pleae have a look there: http://helpx.adobe.com/x-productkb/policy-pricing/activation-deactivation-products.html
If still necessary you could ask here http://helpx.adobe.com/contact.html and if "open" please use chat, I had the best experiences.
Hans-Günter