yup, what they say is so, i just did it.
both parents need to be present to get the passports, or one has to supply a letter giving the other permission to get it. they require their original birth certs (with raised seal) and photos at time of application. childrens' passports are only valid for 5 years. if you intend to do this, get on it soon! you will need to pay extra to super-expedite them.
you will also need a letter giving the non-custodial adult permission for the children to leave the country on the given dates.
so, as Jean said, it will be hard to make it a surprise.
we will be in BZ the same time as you, with our sons. good luck, and enjoy!