My French is terrible, so I reckon your English is just fine 
Your idea of a trigger is fine. Although NOT required I think it is better to write it as:
insert into [server].DB2.dbo.table2
(
col1, col2
)
select col1, col2 from inserted
However, I don't think there is a way to create the action as dynamic SQL - i.e. incorporating the Server name(s) from a configuration table because I don't think it is possible to access [inserted] table from dynamic SQL.
But you might be able to do this in a trigger:
SELECT Col1, Col2
INTO ##MyTempTable
FROM inserted
DECLARE @strSQL varchar(MAX)
SELECT @strSQL = 'INSERT INTO [' + @MyTargetServer + '].DB2.dbo.table2
select col1, col2 from ##MyTempTable'
EXEC (@strSQL)