I'm an insurance agent in AZ. First off, there is no such thing as "full coverage". If you cause an accident with fatalities, trust me, umbrella or not, you will NOT be "fully covered" for that.
An Umbrella policy covers you above your home/auto liability policy. So say you have a major car accident and you have 100/300 liability on your auto. You are sued for 500k. Your auto policy will pay out the 300k, then your umbrella will kick in and pay the remaining 200k. If you did NOT have the umbrella, YOU would be financially responsible to pay the 200k out of pocket.
I suggest you find an independent agent that can shop around for you and explain insurance so you understand what you have/don't have. Don't get insurance online yourself unless you REALLY know what every coverage is for. You don't pay anymore to have an actual agent work for you. Good luck.