I'm a life long Westchester County resident and retired realtor so let me explain some things behind the scenes.
The River towns (especially Irvington, Sleepy Hollow, Dobbs Ferry, Tarrytown, etc.) has been a really hot housing market for the past 2 - 3 years so I can see attorneys, realtors, etc. being busy with clients. Articles in the local newspaper about it probably escalated it.
At this point, what stage are you in? Have both parties signed a contract yet? Did you just submit an offer and waiting to meet with your attorney to give the deposit check? Is this a For Sale By Owner listing or is the owner / seller listed with a brokerage? Are you being represented by a realtor?
The reason I would need answers to the above questions is I'm confused by the attorney issue. In the New York City area, it's required that BOTH parties have their own attorney to represent them. Therefore, you cannot use the same attorney as the seller. The other issue is you did not state if a contract has been signed or not or if you just submitted an offer.