northend:
Three weeks is a great accomplishment, but it's a bit soon to be expecting anything by way of relationship repair. Even if much of what your mother thinks is untrue, enough of it IS true that you don't have any credibility at this point, and you won't have any until you have a longer track record.
The best you can do at this point is to stick to your own path and not worry too much about what your mother thinks. The only antidote here is time and consistency on your part.
Even then, she may never believe you. That is just something that some of us have to live with.