It probably is not a good idea to shave your cat's fur in the rear end area. It would make it 'itchy' when it grows back in, and possibly causes more irritation. If she is stressed out, have you asked your vet if she should be on any kind of medication?
How much stool is sticking to her rear end? My cats all have a slight bit, once in a while that sticks to their rears, but usually in their grooming habits, they take care of it themselves. Is your cat overweight by any chance?
I would make sure that she is pooping normally, with firm, but not mushy stools. If you feed her a good quality food, if you are not at this time, and give her both canned and dry, and plenty of fresh water, it may change her stool consistency, so that it is not so 'pastie' or sticky on her rear end.
The best thing I would recommend at this time is to get some soft wipes, or paper towels, and wet them with warm water, or a soft face towel, wet with warm water, and just lift her tail and clean her butt off as well as you can. You say she is good with you and your mom, so this should not be a problem. Rather than giving her a whole bath, try to keep that area as clean as possible with warm water. I would not keep bathing her, as you can cause loss of oils in her skin that help protect her fur, and if she hates a bath, it doesn't help her or you, and she may end up with behavioral problems towards you and your mom.
God bless and good luck!