Well done for making progress in finding a place to live and having a strategy for disengagement with the JW org.
It sounds like you want to make your case clear to your family by writing to them and since you know your situation better than we do, it probably will sort out those in sympathy with you and clarify your position. If you went back to get reinstated followed by a fade; surely that would be giving some credit to the non-existent JW authority? Is that why your mother favours it...or can she not bear the shame of her offspring being being d/f? And what a time wasting palava to go through reinstatement!
Hold your head high, you have done no wrong to disagree with a harmful cult.
Although not knowing your age, there are three things, might I suggest, which will be important for you to have: positive thinking non JW friends, a good educational attainment and a goal (or in your case a target!)