Tableau Reader is a great tool to share packaged workbooks, but in this circumstance I don't think it is what you are looking for. I say this because you mentioned wanting to restrict access to parts of the data source, and parts of the dashboard.
Tableau Reader only runs off packaged workbooks (aka .twbx files), and therefore only runs off of data extracts. It cannot use a live data source, or a data source that is published to Tableau Server.
Row Level Security depends on the end-user having a Tableau Server username. To be more specific, Row level security works by doing a simple Boolean check comparing a user’s Tableau Server user name to their name in a "security table" contained in the data source. Without a Tableau Server username, users would be able to see no data. If fact, if you look at the "Restrict Data Access..." article linked above, the first sentence says that these methods only work "by publishing them to Tableau Server or Online".
Another thing to think about is, what if your end-user has a copy of Tableau Desktop? Then they could just open your packaged workbook in Tableau Desktop, and it would be very easy for them to remove any user based filters or row level security you have implemented. At that point they would have access to all the data, and to the entire dashboard.
The only way to achieve your goal with Tableau Reader would be to create a dashboard and data extract that is customized to each end-user, containing only the data that they have purchased from you. Unless you have a very small amount of end-users, this would be a time consuming task.
The use case you are describing is exactly why Tableau Server was created.
Yes, I agree. Tableau Server is the option for you. You could also look into Tableau Online if you don't want to manage your own Tableau Server instance.
There is a way to achieve what you are saying by using the APIs, web mash up and Tableau Public account. We implemented a solution for a client who wanted to share dashboards to multiple clients but wanted to secure the content and which view is shown to which customer. The key is security and the right user account management with Tableau APIs configured correctly to work with your website. Pl. write to me at email@example.com if you need further information.