Do you obtain the reward of the congregation if you pray the obligatory prayer individually at the beginning of its time, then pray a missed prayer in congregation with your family?

You will be rewarded for leading your family in congregational prayer for the missed prayers you are making up. They will also receive the reward for congregational prayer. It is permissible for someone performing a prayer on time to lead someone making up a missed prayer, and vice versa. However, it is better to avoid this to steer clear of scholarly disagreement. You can make up the missed prayers at the beginning of the prayer time and then lead them, or you can pray individually at the beginning of the time and have someone else lead them; congregational prayer is not obligatory for women, but it is recommended for them.