This is one of those times when a mistake is literally "cast in concrete." But that doesn't mean a complete tear out and do-over is required to remedy the problem. They need to excavate, cut and remove sections of the existing foundation and pour new footings and walls properly mated to the existing ones and properly waterproofed. That's where the engineer comes in.
If the engineer is a licensed professional engineer (and your state's laws should require that) I wouldn't worry too much if the builder is cutting their check. A licensed engineer isn't going to put his/her license, professional reputation, and future earning potential at risk to design a less than appropriate solution for your foundation in order to save the builder a couple of bucks.
For folks wondering how to prevent a similar mistake on their own project, it's fairly simple: 1.) have a surveyor produce a site development plan which shows the location of the home, driveway, walks, etc. shown in relation to property boundaries and building set-backs, and 2.) have the surveyor layout the excavation as per the site development plan before any excavation work begins. Many lenders require a foundation survey as proof it was constructed in conformance with the site development plan before dispersing funds to the builder.
Q
Great idea!
Q