Try to think outside the box, leaving the lawyers out of the picture, at least for now. Unless your parents are wealthy.
If there is proper documentation (dated photos, copy of contract with warranty, etc.) that prove the concrete failed and is unacceptable, you or your parents should present the documentation, first to the contractor, then to the local or state licensing agency which oversees the building trades in their area. You or they will be required to complete and submit a form or forms describing the situation, and have specifics as to what is expected to make the work acceptable. And it wouldn't hurt to present their case to the local BBB, and even Angie's List--bad PR can be a significant motivator if all else fails.