Describe the family that appears in the photograph!
I see a mother, a father and two childrens - a girl and a boy.
There're limited number of cases when you can blow article away. "A girl and a boy" it is not one of them.
You cannot use "the" at the first sentence when mother and father are not described.
To add to the comments above: "children" is plural, so you don't need to add -s.
Well done! Keep learning!