Anxiety Support Group
Anxiety is a physical condition marked by intense and persistent feelings of distress, fear, angst or dread. General anxiety caused by routine day-to-day stresses usually passes quickly and is experienced by almost everyone at one time or another. However, such feelings that linger over time and are very difficult to cope with, and which lack a clear cause, may indicate...

You never know how you'll react until you've been there and even then, circumstances will be at least a little different for everybody who has been through anything similar. Mine certainly were. My father was a criminal league perv.
A couple of wonders wandered through my just-a-patient mind while I read your post:
How was your relationship with your father before your cousin told you her story? Do you feel like you could talk to him about it? How is your relationship with your cousin?
Dunno if those are pertinent to your case, or not. Just wondering. . .
I mostly wanted to welcome you aboard.
Often, it is not what is said, it is different. So, do NOT take it as your problem. It is not your problem.
I have found that when people share that information, often they have an ulterior motive.
I kept my mouth shut when ... were flying around about someone I am close to. When the dust finally settled, it was revealed that the person who actually did the criminal act was someone else. Evidence was presented at a huge family gathering and everyone there stood up and told the person who was falsely accused they were sorry for what happened, and they would support whatever action was taken.
If you have a decent relationship with your dad, keep it. If your relationship is strained, do not add this situation to it.
In other words, leave it alone unless you have a specific issue involving your self with this.
Best wishes.