This all depends on the cause of why she no longer wants to go out with you. Based on what we know about dogs and their aversion to anger, it is pretty safe to assume that your deduction is accurate or at least a step in the right direction; dogs are naturally inclined to avoid anger, as an instinct to avoid potential danger or to avoid possible decay in their relationship with us, as creatures dependent on our care and thus at the whims of if we decide we no longer want to.
Therefore, the answer is
- Avoiding the aversion trigger
Patience: You need to assume the perspective that basically, your dog does not fully understand human speech or concepts such as, say, a bad day at work, or being exhausted when first coming home. While that's a no-brainer on the surface, the problem a lot of owners face is that they expect training to work at a pace that makes sense to humans. Why wouldn't she get over it? It's been this long and you haven't repeated the behavior again, so shouldn't she understand that it won't happen again?
The problem is, because your dog doesn't understand human speech or understand what happened, she doesn't have an explanation that makes sense in "dog logic." Therefore, the safest behavior for her is to just avoid it completely, even if it seems like it won't happen again. If you did touched a lamp and it suddenly shocked you, but you can't find any explanation for why it happened, no exposed wires, et cetera, would you assume it was a one-time thing and decide it was safe to keep touching the lamp? Most people would worry that it may shock them again, and would avoid using it, which creates a negative cycle where by avoiding it, you can't actually prove to yourself that it is safe.
Which is why counter-conditioning is also important. Counter-conditioning (and desensitization) means you train your dog to have a different perspective about the aversion trigger (going out with you) so that it no longer seems like something to avoid. This is a two-fold training method, which means you need to change how she feels about going out with you (the counter-conditioning), as well as show her that it's safe to do so by "proving" that it's safe (desensitization). There are a few ways that you could do this, and it will all depend on what works best for you.
My approach would be to create opportunities to display positive emotion and provide rewards during the process of going outside. You could leave the door open and sit outside, without prompting her or trying to make her go outside with you. Throw a toy around or shake a bag of treats, without necessarily looking at her. Act like you are just hanging out having a good time by yourself. You want her to come out on her own, rather than it being part of the act of you taking her outside. When she comes outside on her own, give her lots of praise, pet her, give her a treat, et cetera. Warm her up to the concept that going outside in your presence is something that she wants to do. You can then build off of that such as, five-ten seconds after your mother has taken your dog outside (while they are still outside), go outside as well. Again, make it very positive with rewards and praise. Eventually, it will reach a point where you can then go outside at the same time as your mother and dog, and from there, you can escalate to trying to take her outside on your own.
However, all of the counter-conditioning will be ineffective and the original issue will be made worse if you don't avoid the aversion trigger. In this case, that would mean getting angry with your dog, expressing frustration during the training process, being negative while going outside with her, or even trying to force her to do what you want during the training. You may have noticed that when I discussed my approach to this situation, I mentioned shaking the treats without looking at her. This is because actions that make it more "obvious" that you want the dog to come outside with you may set off her alarm bells and make her avoid it, even if it seems non-threatening. You almost want to "trick" her into coming outside by making it seem as different from the time you took her out in the past.
I would especially warn against continuing to try to get her to do something if it seems like she's not ready for it.
Example: you have made a lot of progress by going outside with your mom and the dog together, and have decided to try to take her out on your own. However, she still seems nervous, and doesn't come when you call her or backs away from the door.
You may feel like you should keep trying, but the key is to stop trying and let it go. Go back to one of the previous methods, such as leaving the door open and going out by yourself and waiting for her to come out on her own. The more attention you try to draw to it, the more her instincts will recognize this as similar to the situation that she previously felt negative towards, and will want to avoid, meaning you sabotage your own progress in training her.
I wish you the best of the luck, friend, and hope you are able to work through this. It's hard to predict how animals will react to things, and the best we can do is just show them that it's safe and that we really don't mean any harm.