Private lessons are for all levels of ability and are much more flexible than the group lessons, however they will work out more expensive.
You can choose from 1 on 1 tuition or you can even have 2,3,4 or 5 friends all in the same private group. If you want to have a private instructor for more than one person, let's say you are a group of four friends - you need to make sure everyone is of the same ability as otherwise it defeats the object of a private lesson as the instructor can only teach to the least standard in the group.
However nice it is to go skiing with your kids, if you decide to get a private instructor for your family, if the children are younger than about 12, it's best to get them a seperate instructor, basically kids normally learn a lot faster than adults and by insisting you ski with them in the group you can actually slow down their progress. Instructors also have different teaching methods for younger kids to make it more fun as well. Remember you will have plenty of time before or after your lesson to go out skiing together on the slopes (but be prepared, your kids will be better than you)