Percent chance of mountain lions or other wildlife that will hurt my family?

I would say unlikely

Bear Mountain do have bears. No mountain lions. Be prepared and bring bear repellent, wear bells. Bears do not attack people unless they are harassed or bothered. Most will stay away from humans. Do NOT carry food with you while hiking,

It is a park where you can go with your family without any problem ,the only animals you can see are in the Bear Mountain Zoo.

Unlikely