Good discussion going on here, and agree with Ryan 100% about informing the business owner of the risks he is taking and, if you choose to continue serving this business, structuring the contract so that you are not responsible for negative outcomes.
One of the major risks I would discuss with the client is this, at least the way I am understanding what you've described.
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The business had a site and built citations for it at location A.
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The business then had you build a second site covering locations A and B and wants you to build citations for business B.
If this is correct, the trouble is that the business now has TWO websites representing the location of Business A and this is pretty much guaranteed to cause holy heck on Google's end. Google wants to find a single authoritative website representing each physical location (each Google+ Local page). Finding 2 authoritative websites representing location A is going to cause confusion and could water down the authority this client has built for business A, decreasing the benefits he's earned. The client needs to hear this.
Ideally what should be happening here is that:
A) The customer fully separates out his two businesses, legally. He runs 2 different companies out of 2 different offices with no connection between them. He runs 2 different websites and supports them with 2 unique citation sets. This would be the above-board, risk-free approach.
B) If the customer will not do this, then I agree that he is making a poor choice in trying to make a single company seem like 2 different businesses, doubtless for SEO purposes. I see trouble ahead for the business if this is their approach to marketing. It's possible that you could continue to work on the site you built, removing ALL references to the location of business A and only building citations for location B, but without knowing all of the nuances of this, it seems pretty iffy to me.
I totally sympathize with the pickle you're in on this, not having realized what the company was doing before you developed their new website. You could choose to walk away from the contract if you are not comfortable moving forward. I'd personally be tempted to do so, if the client refused to act on my marketing advice regarding this. At the very least, the one thing you have learned from this is to structure into your initial client discovery form questions regarding all sites they currently own. This is a hard way to learn this - but an important lesson, for sure.