I can totally understand your frustration. You really just need to decide what you want to do. My dog, Daisy, is a bird dog. I took her to my friend's home and my friend made the mistake of letting her out while there were still a few chickens loose. She took off straight after the first thing she saw running, which was her rooster. Daisy is very well behaved, eager to please, and well trained... to an extent. I haven't even had her a year yet. We adopted her from a shelter where she had sat for a long time because she's old, big, and black. She's 9 years old now and gets pain in her hips after too much exercise. My friend really didn't think she would do anything or even be able to. Daisy is strong, fast, and smart. She had some good training to start with but clearly didn't learn as much as she was capable of. I have been working with her on a pinch collar to train her around exciting distracting situations so she will listen to me and not her own instinct. It took a few months after we got her, but I can easily get her to sit by the door and stay while I leave the house without her rushing the door to get out.
My point is this, if the dog is trainable, and you love your dog, then taking the time to train is worth it. She still gets watery mouth when she hears the babies cheeping, but she doesn't act on her urge. She will sit at the door with it open while I"m in the bathroom playing with them.