you probably need to simply join three groups of data together to create your view; it might be slow;
CREATE VIEW vwGeneralTransactionsMultiSite
AS
SELECT T1.Site,
T1.Trans_num,
T2.*
FROM GeneralTransactions
INNER JOIN Site1DB.dbo.GetDetails T2
ON T1.trans_num = T2.trans_num
AND T1.Site = 'Site1'
UNION ALL
SELECT T1.Site,
T1.Trans_num,
T2.*
FROM GeneralTransactions
INNER JOIN Site2DB.dbo.GetDetails T2
ON T1.trans_num = T2.trans_num
AND T1.Site = 'Site2'
UNION ALL
SELECT T1.Site,
T1.Trans_num,
T2.*
FROM GeneralTransactions
INNER JOIN Site3DB.dbo.GetDetails T2
ON T1.trans_num = T2.trans_num
AND T1.Site = 'Site3'
Lowell