Hi,
I think that it can be done with HikaShop, don't allow the customer to access the whole website but only the product (for example: access website) if his group is only registered, create a new group, for example "allowed".
In the product edition page, set the option "User group after purchase" to "allowed". By this way the customer who bought the product is in the group "allowed" and can access the whole website.
For the temporary access (one or two days) I think that you will have to made a plugin to remove the group to the user if he's in this group since more than one or two days. There is maybe already a plugin in Joomla for that.