Your post contains two issues.
As to your ex quitting her job, Connecticut uses an earnings capacity rationale in setting child support. Under this argument, if the person is earning less than their earning capacity, child support is set at the level dictated by capacity, not by current earnings.
You need to show that she quit to avoid paying child support. I can expound on this later but basically, unless it was the world’s worst job, she’s gonna need a real good excuse for quitting at about the same time she lost custody.
As for your second issue – the arrearage vs. the child support, the big question is whether the judge’s decision is based upon statute. If the decision not to credit the child care payment against the back award is grounded in statute, courts will be very reluctant to make policy.
As a practical matter, why don’t you trade off the arrearage of $28,000 against what you are trying to get out of the ex? Maybe she would agree to drop the demand for the $28,000 in return for your not asking for support.