rehoming pets?

Grace • cant wait to meet my little lady 🎀
Have any of you had to rehome your pet because of your baby? Please give advice!! 
I am someone who STRONGLY believes pets are family. I have never adopted a pet and not kept them for the rest of their life. That being said, I am on my absolute last straw with our dog. I adopted her when she was 12 weeks old, she is a jack russell and we have put in SO MUCH time and effort trying to train her. She is 4 years old and she is an absolute train wreck. She barks at anything and everything, does not listen to ANY command we give her except sometimes she will sit (very rarely). We have another dog that I adopted about a year ago, she is also 4 and she is wonderfully behaved. The jack russell attacks the German Shepard constantly, runs up and bites her face literally any time the German Shepard goes to get a drink, gets on or off the bed or couch, goes to lay in her bed, goes to go outside or come inside, comes over to get pet by somebody, literally even if she just shifts positions or goes to scratch herself the freaking jack Russell is is right there biting at her face. The German Shepard literally does nothing to her except sometimes will growl when she's really fed up with it. The jack Russell has began taking baby clothes, baby toys, any baby item and will run off with it and growl when I go to take it from her. My baby isn't here yet, I'm due in a week and I've been trying to crack down on training through my entire pregnancy (before that too but especially once I got pregnant) and she is making no progress. I've tried everything with her. We are currently staying with my boyfriends grandma for the last month until the baby comes and the jack Russell is constantly jumping up on this poor frail old woman and scratching her to try and get pet or snagging food from her or just compulsively licking her. 
I normally would never rehome a pet but I have tried every training trick out there short of actually hiring a dog trainer to come work with her (which I would do if I could afford it but it's not an option) and she makes NO progress. She gets tons of exercise and is on a healthy diet. 
I honestly am nervous to even have her around my baby because I know she's going to either be aggressive like she is towards my other dog or she's going to scratch at her or just be rough or jump on me while I'm holding her or something. I don't want to risk it and I want this dog gonnnne. The problem is my boyfriend loves this dog and is blind to how awful she is. He makes excuse after excuse for why she's so dysfunctional. I'm going to be so over protective of this baby so make sure this lunatic dog doesn't get a chance to do anything but gosh I'm desperate to rehome her. I guess my question is have any of you been through something similar? I don't know how to get my boyfriend on board with rehoming her. Any advice?