Yes , outside of Bridgette, and Ethlin the girls will inherit what ever items that they can equip from their mother's inventory and vice versa the boys will inherit anything that they can equip from their father's inventory . In Bridgette's and Ethlin's case ,however, they're sons will inherit their equipment and their daughters will inherit their father's equipment. Ex. Ethlin is holding a light sword before the end of 1st generation in the 2nd generation leaf comes with the light sword . Also it's important to keep weapon rank in mind children can only inherit equipment they can equip .