"If the nodes on the Primary site failed accidentally, VM unable to be online on the Primary site, then the VMs will try to live migrate to DR site."
If the primary site fails, it is impossible to live migrate to the DR site. Live migration requires that both ends of the migration be active.
"when I make shutdown to the vm at the hyper v cluster the VM at the DR site RUN automatic"
How are things configured at both sites? If you manually shut down a VM on the primary site, you can write a script to automatically start the backup VM at the DR site. Scripting will work for either a live migration or using Hyper-V Replica. Understanding your configuration will help us direct you to the best method.