I know it's probably not what you want to hear, but it sounds totally typical. My kids are 2.5 yrs apart, and this sounds like their typical interactions at that age. Even now there is a low level competition vibe between them, despite my best efforts to reassure both of them, etc. I never "tolerated" them being paritcularly grabby or mean or whatever, but I also was not able to prevent them from doing it, and the gentle, firm ways I addressed it did not sink in for a long, long time. My kids seem to take a long, long time to learn lessons. It's sure not for lack of trying, it's just that they are very opinionated and very persistent. I wish they learned lessons easily, but they require dozens and dozens of times of guiding through interactions before the ideas even start to trickle into their brains.
I wish you good luck for the remainder of the visit!