Sometimes it seams like a great idea for two people to learn an instrument together and while it sounds fun, it can defeat the benefit of a truly private lesson. Differences in ages and learning styles make it hard for this to be a reality.
Our experience has been that both students will naturally progress at different rates. Learning how to play a musical experience is a joyful experience and gentle encouragement is always an added plus.
Parents that take separately from their son/daughter are still able to encourage during lessons and gain the knowledge to help during private practice time from what they have learned. An added bonus is spending more time together and being able to schedule a once or week private practice time where you can share what you have learned with each other and maybe play duets!