It is best to use will when you refer to future events. I will read more in the language I am studying.
The use of going is substandard but commonly used. It should not be combined with will when both are used to mean the future.
It is fine to say that you will go to the store. Will is used for the future and go is the physical act of performing the task.
Try simply saying that you will pick up your children.
Also note that the children at now at school. You may pick them up from school.