DECLARE @A_ROCK int, @A_HARD_PLACE int
SET @A_ROCK = 2345
SET @A_HARD_PLACE = 45678

SELECT A, B, C
FROM (
        SELECT A, B
        FROM dbo.mydb1
        WHERE B NOT IN ( SELECT B FROM dbo.yourdatabase) AND
                A IN ( SELECT A FROM dbo.theirdatabase)
) AS DB1 LEFT OUTER JOIN (
        SELECT C
        FROM dbo.yourdb1
        WHERE C IN ( SELECT C FROM dbo.ourdatabase) AND
                C BETWEEN @A_ROCK AND @A_HARD_PLACE
) AS DB2
        ON DB1.A LIKE '%'+DB2.C+'%'
WHERE DB1.A BETWEEN @A_ROCK AND @A_HARD_PLACE AND
        DB2.C NOT IN (SELECT A FROM dbo.mydb2)