My understanding is that you are not combining data from 4 different servers as your data source in this report, correct?
Then, In ReportManager - go to report properties - i.e. right-click on your report and then left-click on Manage from the dropdown menu. Then choose Data Source tab - it will have the following option:
A custom data source
Data source type: Microsoft SQL Server
Connection string: Data Source=YOUR.SERVER.IP.ADDRESS;Initial Catalog=YOUR_DATABASE_NAME
Then choose: Connect using: Credentials stored securely in the report server
You can enter your domain username and password there: e.g.
User name: SOMEDOMAIN\MyUser.Name
Password: MyPa$$wo%d
Then checkmark: Use as Windows credentials when connecting to the data source
You may need to checkmark this one too: Impersonate the authenticated user after a connection has been made to the data source
This will store your login/password combination securely on the server and will allow the report to connect to your datasource.
You can also do this for a shared datasource.
Otherwise, If you're trying to combine data from your 3 servers and 1 additional where you have read-only access only, I would recommend to:
create a linked server entry on one of your servers pointing to that 1 read-only server, and may be two more for the two other servers
create stored procedures that would provide datasets for your report gathering data from the other 3 servers as needed - this way you'd only need 1 datasource on the reportserver
Does this answer your question?