"Your children write a book."
Translation:Tes enfants écrivent un livre.
Enfants is really the proper translation for children. And as for infants, I'm not really sure that they would be able to write books, because If I'm not making any mistakes, infants is generally used for very young children. "Sons" in french is "Fils", and specifically adresses only male children.
Concerning the "It's ok to go with the plural masculine"...well, yeah, but not like that. This rule just states that if you have a mixed group, the masculine will go over the feminine. But that's pretty much it.