Answer: It is ‘normal’ but it does not mean it is wise. In fact, worrying not only does not make any matters better, it has a tendency to worsen things, by imagining too many things that are most likely not going to happen, thus making oneself lose peace of mind, while overly bothering the person worried about, which also makes the person lose peace of mind. This is how everyone’s blessings are as if reduced.
The Buddhist approach for handling worry by Shantideva is simple. If there is something that can be done to resolve the matter worried over, just do it, instead of worrying, that does not help at all. If there is nothing that can be done to resolve the matter worried over, just let it go, instead of worrying, that does not help at all. It is freedom from worry that brings about peace of mind, which is a basic blessing that we all need.
Question: It seems unfair if my children are ‘punished’ because of my worrying?
Answer: If you feel that it is unfair, you should simply stop worrying. As the karma of parents and their children have some collective intertwined nature, your children might be karmically punished by your worrying, only if it bothers them. If it does not bother them, surely it is of no worry to them. It would just be self-punishment on your part. Either way, again, worry is useless. It is not only unproductive, it is potentially destructive, capable of disabling one to not take control of life to create more blessings, to only remain fretting about this and that to no end for no good reason.