Why is "Dad will bring presents to his children" incorrect? I do understand that it could be some other children, but it could also be "his" children depending on the context, could it not? It could in Russian.
As the sentence says something about some unspecified 'children', it seems too much to assume that this is 'my dad'. After all, then it would rather be "will bring us presents"...
So it is the dad of the subject of the sentence, i.e. those children.
It sounds very odd to use the verb bring rather than give when saying bring to the children. It works with something more abstract like happiness but in this case, it sounds like he might not actually be letting the children have the presents compared to bring the children presents.