The first problem is, with a staunch JW like your mother, there may be nothing you can do to sway her. She is so afraid, if she hears you are reinstated-but-inactive, she may still instruct her children to shun you anyways because you are "bad association".
The second problem is, the elders are not as motivated as you are to restore family relationships. You may end up grovelling for a very long time, only to have the "carrot" moved out of your reach. By the tone of your letters, you sound like a very headstrong and opinionated woman. In other words, a really neat person to know. ....and somebody the elders are terrified of. Are you sure you could keep up the charade for months, years?
If I were you, I would continue to work over the source of the shunning, your mother. Do your best to soften her up. Never, never, never bring up topics of religion. If she can allow a small amount of contact without her congregation finding out, you will have won.
Perhaps a modified approach from what Mary is suggesting might help. Perhaps a tearful letter explaining how sorry you are that you have been such a failure to her, and how it must pain her even to receive the small gifts and money from time to time. In order to stop causing her any more pain, offer to stop sending these gifts and money from this oh, so disappointing daughter.
