Can I drive my deceased dad's car briefly (but long distance) before telling dealership so they can take it back? ?

No.  Or actually yes, but not in the way that you meant.  You need to talk to a lawyer before you do anything.

Here's why the answer to no:

1. It's not your car and you don't have permission from the owner, so you'd be stealing it.

2. You aren't on the insurance.

3. A loan can't be ended simply by telling the dealership to pick up the car. The money is still owed. Nobody can inherit anything from him until his debts are paid. The lender doesn't just get the car -- they get his bank accounts or whatever else it takes to repay them in full, even if that means that no one in the family gets anything.

Here's why the answer is actually yes, but not in the way that you meant:

1. When one parent dies, the other parent (the one who is still alive) usually gets custody, not the person whom the dead parent wanted.  The wishes of those whom you mention don't really matter.  If the mother is alive, custody would almost certainly go to her, unless she refuses or there is some reason that she can't get custody.  You might be able to go to court and get a judge to award you custody, but it's not easy or simple, and it's definitely not based simply on wishes.  This can be a lengthy and expensive legal battle, especially if the mother wants custody, and certainly won't be resolved before the next car payment is due.

2. For taking a child from one state to another without having permission from a parent who is alive and without having been officially awarded custody in court, you could go to prison for many years.  Even you don't go to prison, it could keep you from getting custody.

If you take both the child and the car, then you might go to the same prison as you would have gone to if you had taken only the child (and not the car).  In that sense, you get away with taking the car.  You might be sentenced to stay there longer than if you had taken only the car, but you also might die there, so the outcome is the same: prison for as long as you can stay alive in prison, then death.  This probably wasn't want you meant.

Try this.  Who is the executor of the estate?  What are the terms of the loan regarding who owns the car now that the loan agreement is terminated by the death of your father?  Was there a death benefit attached to the car loan? The executor needs to determine who owns the car now.  Get the owner's permission. Anything else is car theft. 

You don't have to tell the company anything just tell them my dad loaned me the car a month ago and he died the other day and I'm in California does my dad have credit life insurance on the car? Some companies do have credit life on the car so that if your father dies the loan gets paid off you might be the owner of the car and not even know it but if they say no ask them what do I do with the car.

Immediately speak to your dad's financial lender for the car.  Ask if they can work out a payment plan that you can afford

Ditching the car makes it look as if you did something shady.  I have no idea what could be illegal about this, but I would just call them and have them get it from my place.  Oh, I would definitely do it.  They can sell it in CA to another dealer so I doubt they would be really upset.