Hello Azzam
When you had the failure, did it only affect the multicast traffic or all traffic on your network? If it was all traffic, then the issue will not be with the PIM DR priority, but with a more general issue of configuration. With the information that you are providing, my first instinct is that VRRP has been configured without the use of object tracking. So the Internet-facing interface of the secondary link went down, but that did not affect the VRRP configuration, so packets were still being sent to the switch with the failed link. However, if your routing configuration noticed the change in topology, it may have routed traffic to the other switch and out to the internet. How are your L3 switches connected to the ISP? Are you using BGP on the network edge? It all depends on the configuration and how you have it set up.
Take a look at the following lessons that may help you configure the network edge more appropriately.
If you let us know some more information about your topology, maybe we can help direct you in the troubleshooting procedures.
I hope this has been helpful!
Laz