If something would happen to me (mother) would my 11yr old and 13 yr old have the right to decide who to live with or would they automatically go to the father who hasn't seen or talked to them in a year?

In the absence of a will or guardianship assignment on your part, they would go to the nearest living relative which would be the father. If you don't want him to gain custody, then make a will.

And even with a will, he would have the right to file in court for custody.

But the only way to prevent it at all, is to have a will and custody arrangements made before hand.
And at 11 and 13, they would have a say in court as to their wishes

Now I'm not sure about this. I had talked to a lawyer about this also. I can go a step farther by saying that my son is 8 and I have had SOLE LEGAL AND PHYSICAL CUSTODY of my son since he was born. When I asked the lawyer about this, she said that even if I made a will, the father would get custody and the will would mean nothing in court when pertaining to my son. I asked her why it is this way and she said that it's this way because he is the other parent.

Now she was rude, mean, and a ***** to me, so I really don't completely trust what she has to say.

Shell