Maintaining constraints across different databases

Constraints between tables among different databases are only possible using the Triggers.

The ON UPDATE and ON DELETE rules you can simply implement by the AFTER UPDATE, DELETE triggers. The referential integrity you can enforce by the INSTEAD OF triggers.

There was a similar question in past about this.

You can create a simple AFTER INSERT Trigger, which will insert data to a table in other database.

CREATE TRIGGER dbo.trg_aTable_AI
   ON  dbo.aTable
   AFTER INSERT
AS 
BEGIN
    SET NOCOUNT ON;

    INSERT INTO [otherdb].[dbo].[OtherTable](Col1, Col2)
    SELECT
       Col1,
       Col2
    FROM INSERTED
END
GO