Hi Justin,
Think of the relational ArcGIS Data Store as a database connection on ArcGIS Server. It is a type of managed database connection registered on the federated server. Therefore, it's not possible to register database connections with the Data Store. You can add data such as a feature class/table into it and that is done when you publish hosted feature services with relationships to a standalone table.
I believe you're referring to live data sources as services that use data from registered enterprise geodatabases or databases with ArcGIS Server. The limitation of creating relationships at this point is that you can't join registered feature layers stored outside ArcGIS Data Store on the hosting server.
If I am not mistaken and you can correct me, you're looking to use relationships on data sources that will reflect data that are constantly updated on the geodatabase/database. You can do this by publishing a hosted feature service to your ArcGIS Data Store/Portal once and then update it nightly by using ArcGIS API for Python: Updating your hosted feature services with ArcGIS Pro and the ArcGIS API for Python. This blog contains instructions on how to do this for ArcGIS Online hosted feature services, you can update your connection to Portal and perform these steps for ArcGIS Enterprise as well.
So, with the script updating your data every day and if you create a model in Insights for the relationship between the different datasets, you can just update the model every day in the workbook to give you the updated version of the relationship.
Let us know if you have any other questions.
Thanks,
Aravind