You have mainly three options after setting up you new core server:
1. Install an agent from your new core manually
2. Schedule a push distribution from your new core server to all clients
3. Schedule an advance agent push to all your clients from the new core server
All these three options will move all your clients to the new core server at the same time as update them to service pack 2
If you would like to keep your old core, you can install SP2 on your core and could push the sp2 client update via Patch Manager to your clients.
Nevertheless, you need to reinstall your agent or just push the sp2 to your clients, depending if you want to keep your old core or move to a new one.
Regards
Schmiddi