An example of a file format that you can use as a bridge between AutoCAD, and many other CAD applications in general, and QGIS is DXF ASCII 2010.
DXF is sort of a universal file format designed for this purpose, but you can't forget that there are many versions of it - 2010 always works for me.
Regarding being frustrated with the client, and how to design a data workflow that works for both of you... that is more of a general consulting question rather than a QGIS question. Clients are valuable for many of us - if you don't see it that way, maybe you'd benefit from taking a short break and thinking if the job you're doing is fulfilling enough to keep doing it for a long time. On occasions, it may end up being a bit frustrating working with some other person if you don't understand each other's expectations well. Maybe your counterpart knows very little about GIS, surveying and map projections, and expects you to 'solve all of their problems' regarding surveying and mapping. Sitting down with them and explaining the data requirements or minimum needs for you to be able to do the mapping may be able to solve it all. As some people call it, you can "educate your client". Or maybe you can recommend a good surveyor that can help them and help you by doing the field work and providing data in a suitable format?
Hope it helps.