Why this is the best way to support your children?
First, parents are the role models at home. Good or bad, your children look up to you. If you study hard, study everyday, play chess everyday, and accept losses gracefully, your child will see it and will try to follow your example. Action is much more effective in teaching than words.
Second, you will appreciate more the toughness of the game, and much easier to sympathize your child when s/he loses. You will understand him/her better and not jump to conclusion.
Third, with a common interest, you and your child can spend more time together, hopefully improve the communication between parents and children. You can have fun time together, and survive the long depressing plateau together.