I apologize - this is very long but is a step-by-step way I train dogs with door darting issues. As far as the door darting, it is possible to get a dog to change that behavior but I'll be honest, it takes work and repetition. It takes you staying in training mode, matter-of-fact and not losing patience as it is hard to train the greeting excitement reaction out of a dog. To train her from the start, use high value treats she will "kill" to get - her very fav's that she sits up and takes notice over - something like turkey hot dog pieces or boiled chicken. Desensitize and redirect her energies to the door by repetition of having a family member knock on the door/ring the bell, take a treat in your closed fist and guide her after your fist carried low beside you near her nose to a spot you want her to go to when someone is at the door. Make it a spot where she can see who is at the door - don't frustrate her by putting her in another room. Let her door spot be within sight of the door and the newcomer. Anyway, guide her with the closed fist full of a treat to the spot you want her to go to, have her lie down and treat her, rub her back in praise and smile. No excitement here. Don't amp her up by wild praise here. Just treat and praise when she lies down. Keep repeating this over and over - at least 4 - 5 minutes at a time a few times a day.
At the same time, if she doesn't know the "stay" or "wait" obedience trick, teach her that and keep the training fun and upbeat. You want her coming along happily with the learning process. Smile when she gets it right. Praise with really loving feeling, looking her in the eyes and treating. This will help her start to learn there is such a thing in her life as impulse control and that if she goes to and waits in place when someone comes to the door, she gets that lovely treat. Here's the trick - don't treat every single time after the first few days of training. That expectation of when she might get a treat is wonderful to dogs and they work hard in hopes that this might be the time. It is more effective than treating every time after the first few days of teaching a trick.
Once she is able to control herself and has learned the "stay", start to desensitize her to staying in place in her door spot, the place you are teaching her to go for a treat when someone comes to the door. When the doorbell rings and she goes to her door spot of your choice and lies down, treat her and say "Stay" or "Wait", hold her eyes with yours and hold that treat in your fist before her as someone else answers the door and lets the person in. Herd her back into place when she tries to get up and go greet. And she will. Over and over she will try. THIS IS WHERE SHE WILL TRY YOUR PATIENCE TO THE DEATH! And here is where the success comes in - just stay in training mode, say "Uh oh", go retrieve her, herd her back with your arms and hands outstretched to the side, looking into her eyes with intent, and when she is backing off, grab a treat from your waited treatbag and guide her with that fisted treat back to her door spot and treat her instantly when she lies down. Say "Stay" again, holding another treat enclosed in your fist before her, holding her eyes with yours. When she does stay for as long as even 1/2 a minute, treat and praise her with a gentle pat, smile and release her with the word "release". Now she can go greet the newcomer. Gradually increase her "stay" times in her door spot before you release and allow greeting. Repeat. Repeat. Repeat. Stay upbeat, fun, smiling.
Repeating this process over and over with patience, love and gentleness is how you can help your dog achieve impulse control and desensitize to the whole idea of a visitor coming to the door without her going wild. It is EXTREMELY work intensive and requires you to absolutely keep it fun and rewarding for her, staying patient and never losing your cool because I find this is the single hardest thing to teach a dog and keep it reinforced.
In the natural world, the dog's impulse is to greet newcomers to the pack, go and sniff the behind, lick the lips of the other dog and often they will jump up on people trying to get to the lips to greet as in the wild. But this process of teaching the long down "stay", the controlling of her impulse to get up and working to stay down to get that reward of the treat and your smile and pleasure - that will go a long way toward helping her concurrently learn to stay down in her "door spot" as a new visitor comes in. EVENTUALLY, she will get that going to her spot, staying down gets her rewards and she will still get to go greet the newcomer, but only after the "release".
In the natural world, the dog's impulse is to greet newcomers to the pack, go and sniff the behind, lick the lips of the other dog and often they will jump up on people trying to get to the lips to greet as in the wild, though in that wild setting with other dogs they don't need to jump up unless they are small puppies. But this process of teaching the long down "stay", the controlling of her impulse to get up and working to stay down to get that reward of the treat and your smile and pleasure - that will go a long way toward helping her concurrently learn to stay down in her "door spot" as a new visitor comes in. EVENTUALLY, she will get that going to her spot, staying down gets her rewards and she will still get to go greet the newcomer, but only after the "release".
It is a
lot of work and takes about a year if you don't work at it a lot but one day it will all come together and you will have a dog that controls its impulse to dart out the door just like dogs control their impulse to bite, pee where they want, walk beside you on the leash and not pull you down the street - all of those things they learn to do despite their natural inclination. But training them to stay calm and in a safe spot as the door open is entirely possible if you keep patiently at it over and over and over, keep it fun and loving and don't give up. Most people give up and give in to the dog's way and go buy gates. haha.
This type of training or some modified form of it is not for the faint of heart and really only for those who love to work with dogs and keep it fun, positive and rewarding and are far more determined than the dog.