In most circumstances, when the will is read (in private, days or weeks after death, by a lawyer - those "reading of the will" ceremonies in books and movies exist mainly in books and movies, I'm afraid) the children will already have guardians and the courts may not wish to move them.
Guardianships, funeral instructions, and personal health directives should never, NEVER be in a will and should never be put in a safety deposit box. It can take weeks for the executor to get a court order to open the safety deposit box - if anyone knows it exists, where it is, and whose name it's under - and by then the same problem exists.
In fact, it's really a bad idea to have the only copy of your will in your safety deposit box. If you (or for couples, both of you) are killed, who knows that you have a safety deposit box, let alone where it is?