If her hormones are going crazy as it is, the emotional stress of your grandpa won't be doing much to help. It sounds like she's suffering from a mild form of depression/anxiety usually associated with, as you called it, "the change", which is quite normal but, unfortunately for you, doesn't make things any easier. She probably bothers you and not your brother because she knows she'll get a rise from you, she knows you'll argue back, as horrible as that sounds. But it sounds like that's exactly what she wants with all of these mixed feelings shooting all over the place.
If she has nobody to talk to, it's all she can really do to express herself over the whole ordeal, and whilst it might be hard for you, it's probably twice as hard for her but she can't say anything about it because she's your mom. She'll see herself as supposed to be the "strong one" to look after you during hard times.
Talk to her, instead of shouting, ask her if she's sure everything is okay. Try to let the little things slide. People say a lot of things in the heat of the moment and I know the whole "you were a mistake" is one of the worst to hear, but her apologising shows she obviously didn't mean it. A lot of the time that line comes when the parents sees a lot of themself in their kid and are really aiming their anger indirectly at themselves. Despite how it comes across.
A lot of parents find it difficult to express that they're proud of them, to their children, that they're pleased with how they turned out, that they love them. But just because they don't say it doesn't mean they don't feel it. Anyone with older siblings are always stuck to walk in their shadows, they just have to try to not let it get to them and live their own life how they want. Constantly comparing yourself to someone else doesn't help you get where you want. Wanting to do it despite it, does.
As my mom says to me, "I'm still an eighteen year old in my head, it's just my body that can't keep up and it's frustrating".