That may be counter productive.
If you send those letters, the people you send them to may simply see it as confirmation that you're an apostate. Such letters may sound one way to you and completely different to someone else, and you may say things you'll later regret.
If you're reinstated, that will remove the stigma of excommunication (and allow people to communicate with you), but it sounds as though your mom's on to you.
You may just want to consider a clean break. The greatest weakness of the JW movement is that it claims to represent God, yet there is not a single instance of God communicating anything to the Society, one way or the other. They quote Matthew 24 about the faithful and discreet slave who, when the Lord comes, will find him distributing spiritual food to the Lord's household. So they appointed themselves the Lord's faithful slave. But since the Lord allegedly came in 1914, technically this servant's duties should have already been fulfilled.
The Lord stated that when He returns, He will reject self-appointed servants, saying, "I never knew you!" And He gave the parable of the blind guides leading the blind, an obvious reference to false teachers leading foolish followers, neither of which receive revelation from God.
Your best bet might be just making a clean break. Staying in it will destroy you emotionally and spiritually.