Insert you first table with the new keys (leave the pk blank on insert) and make a (temporary) col in the DB1 table for the old key. lookup (join) your second insert on the old key column to get your new fk. When your done delete the old key column and your done.
Here is the sql:
CREATE TABLE DB1.Group(
GroupID [int] IDENTITY(1,1) NOT NULL,
[Company] [varchar](10) NOT NULL,
[Description] [varchar](1000) NOT NULL,
[old_key] [int]
)
CREATE TABLE DB1.Instance(
[InstanceID] [int] IDENTITY(1,1) NOT NULL,
[Description] [varchar](1000) NOT NULL,
[GroupID] [int] NOT NULL,
)
Insert into DB1.Group (Company,Description, old_key)
select Company,Description,GroupID from DB2.Group
Insert into DB1.Instance (Description,GroupID)
select Description, DB1.Group.GroupID
from DB2.Instance join DB1.Group ON DB1.Group.old_key = DB2.Instance.GroupID
ALTER TABLE DB1.Group DROP COLUMN old_key