Family Law Questions? Ask a Family Lawyer Online.
Even if you name a guardian in your will, there is no guarantee that this will be followed. A lot of people refuse to believe this is the case, but the truth is that you are just stating what you would like to see happen... the court does not have to follow it. But the parent's wishes to carry a lot of weight with the court, and are usually followed.
To answer your questions, if the first choice died, it would depend on what had happened between the time they took guardianship and the time they died. It would also depend on the ongoing relationships of the children with your 2nd choice and with the guardian's choice. Basically, at that point, the court would just enter its usual "best interests of the child" standard, and one of the factors in that determination is what you as the parents had wanted. But it would depend on how much time had passed and how old the children were at the time. Their wishes if they are teenagers would probably override their deceased parents wishes at that point.