How is she doing? Did you get a chance to try SQ's suggestion to give her a cheerio to see how she grasps and holds it? Please read LilSpaz's questions and respond when you are able. I'm in the agreeance that the disorientation and unusual arm movements sound like you may be dealing with a Pituitary Adenoma in addition to what else may be going on with your little lady.
Please try to take a look at how her top and bottom teeth are aligned. Did the picture that your Mom consulted with the vet tech show the top and bottom teeth clearly? When you're checking her teeth, are the top and bottom teeth even, straight across and do they touch properly or are the bottom incisors misaligned (eg one longer than the tooth next to it)? Just like SQ mentioned, her jaw may appear crooked because her teeth are overgrown, which requires veterinary intervention so that they can trim her teeth so that they are aligned. She will likely need this treatment for life if there is chronic malocclusion.
The open wound on her lip may have been an abscess that ruptured but since there are so many unknowns whether she had injured it, I wouldn't be comfortable with assuming that this is the cause. If the abscess isnt from a localized injury to the tissue of the lip, the infection could be originating from the bone (could be related to what you're seeing with her "crooked jaw" and/or misaligned teeth) or like SQ suggested, another type of facial infection/abscess. Both require veterinary intervention and antibiotics to treat the infection. Since this is happening in and around the head, you need to be aware that an infection, if left untreated, may travel to the brain and/or cause sepsis which will result in death.
Whether this is malocclusion, a serious bone and/or head abscess or a Pituitary Adenoma (tumor), all of these medical emergencies require a visit to the vet and immediate veterinary treatment. You will not be able to treat her at home if she requires antibiotics or quality of life medications for a pituitary tumor.
I'm going to be straight forward with you since you have said that you are undoubtedly unable to afford veterinary treatment for your girl. You need to call your local animal welfare league or shelter as soon as possible and ask if they have any services or programs that are available that can offer you very minimal cost or free veterinary care. If they do not offer any services like that and they are unable to give you guidance on other options that may be available to you,
you MUST do what is right for the companion animal in your care and surrender your rat to an animal welfare league, animal shelter or to a veterinary office so that she can receive proper veterinary care and treatment.
There is nothing to be embarrassed about, nothing to feel guilty about nor wrong in surrendering her to a shelter or veterinarian. It is absolutely praiseworthy and compassionate to surrender your beloved companion animal to an organization, veterinarian or another person when you are unable to provide proper care and veterinary treatment for them due to financial circumstances.
Please don't intentionally withhold her chance to thrive and live a long and happy life by receiving treatment. Please place her wellbeing and welfare foremost if she is in a medical crisis situation and please consider surrendering her if you absolutely are unable to provide her with proper veterinary care. ❤