No, that is not the right way to deal with the situation, since a charge back is only appropriate in cases of fraud, nonperformance (not merely a dispute over how good or adequate performance was), or unauthorized charges, not when a contractor or repair person is having difficulty making a repair. If you ultimately do not get the transmission fully repaired (or have to expend extra  sums to have get the repairs done) and the repair shop will not reimburse you for costs, your recourse would be to sue them and prove in court that they either intentionally did not do the work or misrepresented their ability to do it, or that they were negligent (careless), which is what caused the problems. However, if the repair shop is competent and is doing what any reasonable such shop would do, and the problem is that the transmission is effectively beyond repair, or that you are being too "picky" about what constitutes shifting properly, then they would not be liable--they would only be liable in the event of some form of wrongdoing, which is why you cannot simply charge back. If you do charge back without good cause, they in turn could sue you or get the charge back reversed.