Playing family politics is an, unfortunately, important game. Look at it this way, even if she doesn't like her sister-in-law, that woman controls her access to her brother. If 50 cents is enough to smooth things over and make her relationship to her brother easier, then it is money well worth spending.
I have 2 step mothers. My father's second wife was an insanely crazy B$%^h, who treated my brother and I horribly growing up. HOWEVER, even though she doesn't call me or send me cards or wish me a happy birthday or anything like that, she has custody of my third little brother, who is 13. In my younger days, especially after her and my father divorced, I felt no obligation to be nice to her. As a result, she refused to let me see my little brother. Having matured a bit, I learned that for the small effort that it takes me to grin and bear it, be nice, and call her on Mother's Day to wish her a happy one, even when I want to say something else instead, she has mellowed out a lot and now lets me see my little bro whenever I want. Same goes with my father's current wife. I have developed a strong relationship with her daughter, who is basically the sister I always wanted growing up. A little bit of niceness to her, even if I don't really feel it, lets me see my little brother when he is visiting them, and also lets me visit my step-sister whenever I want.
Basically, it doesn't take much effort, and I just keep reminding myself that I am the better person. I choose my battles. If pretending to be nice lets me see my family, then it is well worth it, otherwise, I and my younger brother and sister all lose out.
So look at it that way. The role of playing family politics has typically been the role of women, who look at the bigger picture. Family is family, and she is just probably doing what she thinks is necessary to help keep the family together. Its the little things that matter to women, and your wife probably understands that more than you, simply because she is a woman. If I were you, I would understand that, and since its only a 50 cent investment, let her play her role