It is all about the type of dog and training as to whether the dog will, indeed, have a calming effect, and whether the "pluses" outweigh the negatives. Dogs are an immense amount of work, if you are not a neglectful owner. In many ways, they are very much like having toddlers. You must provide training and reinforcement consistently. You must provide enrichment and exercise activities or they become bored, depressed and even destructive.
You must do your research, even when getting a mixed breed dog because certain traits are very much bred into different types of dogs, and will be present, even if it is not a purebred. For example, I would not recommend buying any type of "herding" breed or mix as they require an immense amount of exercise and get joy from "work" which will include herding your children, if they are not allowed to act in some capacity that fills that need.
If all you want is a passive dog that is basically a lapdog, doesn't have a lot of exercise requirements, and is fully available for petting, but doesn't need much else beyond basic needs like fresh food and water, and minimal affection, then consider either a cat or an older dog.