Thanks Kanya. That makes more sense. I would inform the client of the risks, restructure the contract to address those risks, then move ahead as though it is a completely different and non-client business.
In addition to the risks of some sites not wanting to list both businesses (I'm guessing that when people answer the phones from either one they say, "KM Realty") the other site would pretty much fall under the realm of competition if you're only contracted to work on the new site. From that perspective you're obviously not engaged in trying to affect it negatively, but you are trying to rank the new site as highly as possible which could in turn cause the old site to rank lower.
If the client wants you to perform a balancing act between the two, the contract should likely include both sites. Cheers!