Is it advisable to have adults and children in the same class?

The first things to consider when thinking about ski lessons are firstly your desired goals for the lessons and secondly your budget.

Children and adults tend to have differing preferences for delivery of information and pacing of the lesson.
Adults tend to want detailed explanations of what they attempting, the benefits and how to go about achieving success at the task. They want to attempt, and get frequent feedback on perfecting the task at hand.
Children on the other hand tend to get impatient with lengthy aural communication. They prefer to be given a task and learn by trial and error while attempting the task. They like to keep moving and want the lesson to be dominated by practice time.
This difference in desired communication styles and pace of delivery can often lead to frustration for the individuals involved. Children often get bored in lessons geared towards adults and adults often leave lessons focused on children with many unanswered questions feeling they didn't learn a great deal.
To add to this confusion, children go through stages of development as they grow in terms of their physical, mental and emotional capabilities. A 13 year old would want a very different lesson to a 3 year old of the same ability.
In order for your lesson to be successful you then need to consider the goals of the individuals involved.

Goals

People book ski and snowboard lessons with very different desires.

For example: Is the primary goal the acquisition of skills or perhaps something else like a family experience?
Some parents want to hang out in a lesson with the primary focus of watching their kids progress, others want to have the whole family become as proficient as possible.

If learning to ski or snowboard is the primary focus then optimally the fewer people in the lesson and the closer they are in age and ability the better.
Children and adults should be in separate classes and everyone should be in either individual lessons or grouped in the same abilities.

In the situation where the parents want to make it a family experience and less about learning and progression a family private would work.
The parents and children share the lesson and everyone accepts the diminished rate of skill acquisition as the price to pay to enjoy each others company.
If your kids enjoy doing things with you and are patient in nature this could work well, if however your children easily get bored hanging out with you then this is not your best option.

Budget
Once you have decided what your goals are next you need to consider the budget you have set aside for the lessons.

If learning is the primary focus then, in an ideal world taking lessons individually is the best option.
This allows the lesson to be focused solely on the individual and their desired goals, the delivery and pacing of the lesson is then tailored to the individual.

Although optimal, this however can prove costly if traveling with a large number of individuals. If taking individual lessons is outside of the planned budget then the next best thing is to organize the party into groups of individuals of the same ability and similar ages and goals.
Each specific group then takes a lesson to work on their needs. If this still falls outside the desired budget then taking a cheaper longer lesson and then splitting the time between the various groups could work. For example: Grandma who is a beginner does the first hour, the intermediate kids do the next two and the adult experts do the last two hours of a five hour lesson.

If the primary focus is being together in a family unit then you can just organize lessons based on the time frame desired up to a maximum of 5 people in the class.