Jer. 9:23-24: "Let not the wise man boast of his wisdom or the strong man boast of his strength or the rich man boast of his riches, but let him who boasts boast about this: that he understands and knows me" (NIV).
Apart from knowing God, we have nothing to boast about! All of our abilities and the abilities of our kids are gifts from God, but we can become prideful in how we, or our kids, use these abilities. It's not wrong to be proud of your kids as long as you understand that their talents, and the capacity to use them, are God-given. When we get prideful about their accomplishments, our focus moves from glorifying God to glorifying our kids.
On the other hand, when we are jealous of the talents of other kids, it can be a sign we are longing for the reflected glory that comes from our children's success. Remember, your kids are fearfully and wonderfully made. While other gifts may draw more public adoration, no gifts are more significant or important than the ones especially chosen for your child by God.
Learn to be content with the gifts God gave your children.