If there was a case filed, it is because someone reported it. If the police investigated and the prosecutors' office approved it, charges were filed. If charges were filed, a warrant issued. If a warrant issued, then you were not "wrongfully arrested."
If your mother filed a complaint or called police or sought to be reimbursed by her bank, etc., then she caused the charges to be filed. That she later decided she did not want to pursue charges was not her choice; once the process was started, only the prosecutors' office can decide whether to continue to prosecution or not.
As far a getting the case back before the trial court, you are correct in understanding that the way to do so is to petition for writ of habeas corpus in the trial court, which makes findings of fact and conclusions of law & a recommendation to the Court of Criminal Appeals. The CCA makes the final decision.
You must be able to find a constitutional violation in order to prevail on a habeas petition. It sounds like you are alleging ineffective assistance, and this is a constitutional violation. However, it is absolutely impossible for any attorney to review your case on this forum. A habeas investigation must be conducted, interviews conducted, evidence looked at, the State's file obtained - before anyone can advise you on whether you have a chance.
You will need to hire a lawyer to conduct the habeas investigation, which will then determine if there is cause to file an application for writ of habeas corpus.
Why do you think that you are ineligible for nondisclosure? There is a waiting period after you get off of your probation but you have not stated any reason that you are ineligible. You are ineligible for expungement.
It sounds like you may be eligible for non-disclosure. I would contact an attorney and talk with them about your case and then they can tell you for sure but from what you have indicated I see no reason you can not have a non-disclosure petition done.