". . . The buyers are actually going through a divorce . . ."
You're the Buyer, so you probably really mean the Sellers are doing this!
Regarding the price to offer . . . . remember, if you're financing the deal, then it really doesn't matter what the Sellers agree to, it's what the Appraiser says the property is worth.
You could offer the $265,000 to get the Seller Wife to sign, and then
hope that the Appraiser also sees that the property is worth only $250,000. That could motivate the Seller Wife to get with the program.
The worst thing that could happen is that it's really worth $265,000 or more, and you get the perfect house for a fair price. If it's only perfect for you "if" you can get it for $250,000 . . . . then it sounds like it isn't quite perfect enough.
It's all about motivation. It may be that sub-consciously, the Seller Wife doesn't really want to sell at all, and she'll attempt to sabotage any productive deal that comes along. Agreeing to a price could be just the beginning. Before worrying about her motivation, I'd check in and assess my own. How much do you want this particular house?