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Sorry to hear your dog and partner are having some issues. The best thing to do is book a face-to-face consultation with a behavioral therapist who can watch how you both interact with your dog and how she responds etc. There are so many different possible causes for this behavior that without a face-to-face consultation we could make the issue worse. Attempting to resolve aggressive behavior without a therapist's direct input can actually make the behavior worse and may sadly lead to more serious consequences for both your dog and partner.
First to try to build their bond, have him do some basic training with her so that she is fully responsive to you both. You can use treats or a high-value toy to reward her good behavior. As he is stressed with work, this may sound silly but just taking a few deep breaths and exhaling slowly and allowing our body to relax can really help to release some of the tension and she will be able to pick up on that and should relax a little too.
For the next month or so, really monitor her behavior with your partner to see if she ever shows any subtle signs of concern (standing rigid, staring at him with her tail stiff, etc). Monitoring her like this will help to find out exactly what's causing her behavior (fear, protective, territorial, possessive, defensive, etc) which can further direct training. Eliminate any tug games and try to stop any mouthy behavior (if she has these). You may be able to re-introduce tug games again, but not until they've developed their bond and she is fully responsive to you both.
Never punish her for this aggressive behavior as she won't really understand it and is more likely to escalate the situation, so the goal is to condition her into good behavior (which seems she already has most of the time).
She may have what's called 'social aggression' where she feels she's higher up in the pack than your partner (especially if she was with you before the relationship or because he isn't always there). Essentially, you need to re-establish the order without causing a major aggressive episode. Avoid trying aggressive training tactics (so no alpha rolls, scruff shakes, etc) as these could make her much worse.
Start with the basics, sit, stay, lie down, etc with your partner and you do these together, then with you stepped back until just your dog and partner are doing these together. This will teach her in a gentle way that you and your partner are higher in the social status of your pack than her. Having your partner do more of her daily care routine too will help (feel free to use a basket muzzle to help your partner relax during the early stage). Have him feed her, groom her, hold her leash when he's home. These things will all help to build their bond. At the moment, she may see him as this 'fun but expendable' creature in her pack. So by giving him more of an input in her 'care' and not just in playing games/snuggling etc will help re-teach her this.