When I was growing up we had a Maltese who did similar and would snap at children who tried to pull her around.
But she would take herself off somewhere quiet to be out of their way, and if they went in after her she was known to snap.
Thing is,and I know it’s not PC to say it on here, there are far too many people who think that a dog should be completely tolerant at all times, that the children should be allowed to pull it around/grab it/poke at it and if it snaps it’s dangerous and it’s a slippery slope to a mauling. Personally i think that children should be made to respect animals, and if the dog doesn’t react, the parents should. and that if a dog has taken itself off then they leave it alone,and if they don’t then they face the consequences.
In terms of barking at the door, just how much does she do this. I.e. is it a yap when someone comes to the door or does she let forth and yap yap yap constantly. The former is IMO normal, the latter is irritating. I have a lab who barks at the door, and tbh I don’t stop him. I’m quite happy for people coming to the door to think that I might have a big dog in here. He’s a guide dog and his obedience is 1000% including his recall, so I have no issue with the odd bark. But in truth I also know that bigger dogs barking are less irritating than the yap yap yap of a lapdog.
My dog can be distracted by other dogs. He doesn’t want to go for them, he wants to play with them. If we see a dog then I make him sit, praise him for sitting, put a treat in my hand, and then when the dog has passed and he’s completely relaxed again he gets the treat and the praise. It works perfectly. I do stop when a dog approaches because I know that my dog is under control, whereas I don’t know whether the other dog is. So even if he’s working I will stop him to let the other dog go past.
So sit and praise and treat might be the way to go re wanting to chase things….