There is a high likelihood that anxious adults will pass their anxious chemistry to their children. But don't panic. This is not a death wish for your child. This simply means that some people are more sensitive to danger than others. Therefore, for parents to model facing fears and not letting anxiety boss them around may mean doing some work on themselves first. I have seen many parents come in to discuss their children's struggles with anxiety when they soon realize they face the same challenges. Next there's often a period of mourning, where parents feel guilty about passing on this pain to their children. But there is no reason your children need to suffer the way you have. The earlier they learn the tools to handle life's challenges, the less long-term distress they will experience.
An additional challenge, when you struggle with anxiety and parent an anxious child, is marital strain. One parent (who has struggled with anxiety) may try to protect their child from emotional distress, knowing all too well how bad anxiety feels. The other (less-anxious) parent may accuse the first parent of "babying" their child and of either causing the symptoms or, at the very least, exacerbating them. What often unfolds is a power struggle between the parents, as they attempt to either protect their child or offer up a heaping helping of "tough love." What is often lost in the battle is that they are both right and they are both wrong.
What is necessary to effectively parent an anxious child? Balance. You must push them forward compassionately, despite their protests, while acknowledging just how hard this task is and how brave they are. Nothing likes "all or nothing" thinking more than anxiety. So to shrink anxiety down to size, it's necessary to take a more nuanced approach than all protection or all tough love.
For a parent who has experienced very little anxiety, it may look bewildering that a child is freaking out about a small thing. But that child may be facing a tremendous internal challenge. When our fear brain is activated, our rational brain (otherwise known as the frontal cortex) goes offline. If your child's fear brain is telling her that getting dressed for school is an overwhelming task, screaming at her to get dressed is not going to help. In fact, it will only make her feel more anxious, which will lead to her getting further stuck in inaction mode.
And for the parent who has struggled with his or her own anxiety, don't be too coddling. Yes, your child is feeling true feelings of fear and discomfort, but no, you need not -- and in fact must not -- let fear call the shots. Just because your child is hiding under the covers, stating that school is too hard and he can't handle it does not mean he shouldn't go. When the brain is experiencing a false alarm and overestimating the likelihood of danger, we need to teach the fear brain that it is actually OK and not facing a true threat.
We do this is by facing fear head on. This is no time for words, whether they are of encouragement or threats or motivation. This is a time for action. Anxiety is a slippery slope, and if you give it an inch it will take a mile. Therefore, the best way to nip childhood anxiety is to catch it early and to act compassionately AND aggressively.
For assistance in parenting an anxious child, contact a mental health professional trained in cognitive-behavioral therapy (CBT) or pharmacotherapies, or both. You can search for a therapist in your area on the ADAA website to help you with this challenging, but very important work. Take a look at the self-help materials on the ADAA website, including Facing Panic: Self-Help for People with Panic Attacks.