Children are natural naturists. They are most comfortable in the nude, and don't feel shame of nakedness imposed by the grown-ups.
There are lots of debates going on regarding the impact of family naturism on the children. Each "side" in this debate will always try to find appropriate arguments. It's most important to understand that naturism is not sex, and has nothing to do with it.
While growing-up, a child has to understand what kind of conduct is appropriate and what kind is not, in which way can it be touched, and in which way it shouldn't. Also, a child has to that it is of most importance to tell its parents all that going on in their lives. This is true for all the children, whether in naturist families or not.
However, there is one distinct difference between children grown up in naturist families and those who are not, and this is also confirmed by some studies. It's that children grown up in naturist environment generally have bigger confidence. Naturist children implicitly learn to accept themselves and others. In their early years they understand that human bodies are differently shaped. They learn that it's more important what kind of person you are than whether you look like a model or not. This is a huge advantage of family naturism.
Puberty is the most difficult period while growing up. This is time of intense changes of human body, which puts extra pressure young psyche. In this period of life there are lots of doubts, so it could easily happen that your teenager, brought up in naturist spirit, suddenly starts to insist against nude beaches etc. You should tell them they can stay dressed at the nude beach if they want, but if they're still uncomfortable, maybe it's not a bad idea to spend couple of summers elsewhere. Soon they will be grown up enough to spend summers on their own, and you can return to your usual habits. When this sensitive period is through, they'll go back to naturism with a new perspective. Browsing through the internet, we haven't seen a single testimony of a person that's brought up in a healthy naturist environment who doesn't approve or practice naturism any more. Quite contrary, it's always referenced as a quality.