If your server is changing domain there are 3 things you need to consider:
Authentication - this is based on the domain the server is in. As soon as you move the server from the VIK to BOS domain it will authenticate users to the BOS domain. As an alternative cross-domain trust can be set up at a windows level. This has nothing to do with QlikView.
Authorisation - Are you using NTFS or DMS Authorisation? this will impact what users/groups have access to the applications. Either way you need to ensure the groups/users on the new domain are set up.
Directory service connectors - this is what will connect to the active directory. You have mentioned it has already been changed, so that is probably fine.
And another thing to consider:
the VIK server probably has CALs assigned to users isn the VIK domain. You need to decide whether those uers will be moved to the other QlikView server and assign CALS to their new BOS identities overthere, or whether you want to keep them on the old VIK server and move them toge e ther with the server to the BOS domain. Now for the tricky part: CAL assignments will not automatically move to the new domain when you move your server from VIK to BOS. You will have to manually reassign them. Best hing you can do is define a DSC for both domains (which I think you have done already) and look up the new AD identities using the User Selection dialog. Pay attention to the tooltips when hovering over account names. User names may appear twice without any difference. Until you move your cursor over a name.
The DSC isn't used for much except looking up users in QMC for CAL assignments, distribution lists etc. As Leigh already explained, everything else is handled by the underlying OS and AD.
PS Is anyone on the QlikView server in the VIK domain using Server Objects?