You didn't invite your sister-in-law into the family, however your brother did. She may have other stellar qualities, but having good manners isn't one of those qualities. It is a challenge to maintain goodwill and calm in the face of an in-law's rudeness, and the good news is: remedies are available. While you might not be able to change her behaviour entirely, you don't have to bear the brunt of her surliness. Arm yourself with information, new insights and techniques to keep family gatherings from devolving into chaos.
If you understand the dynamics behind impolite behaviour, you are more likely to achieve a satisfactory conclusion to the problem. One of the best books on the subject is called, "Difficult Conversations" by Douglas Stone, Bruce Patton and Sheila Heen of Harvard University's Negotiation Project. This team has devised practical, easy-to-understand methods for dealing with troubling people and circumstances. Family dynamics are complicated and emotional. You want a satisfactory conclusion to this difficulty with your sister-in-law, not the end of your relationship with your brother.
It's terribly uncomfortable to meet the situation head on, but sometimes the candid approach is best. Do not confront your sister-in-law in front of others. This only makes people jump in and take sides. Other family members may have varying degrees of difficulty with this person, but you do not need their views compounding the issue.
Ask for her help.
Tell her you look forward to family events, and there is obviously a problem between the two of you. Don't say another word until she finishes responding. Give her the chance to explain. Listen attentively and without overt physical hostility. Don't cross your arms or frown and especially don't roll your eyes at her response. Ask questions. Be curious. If it was your child or your best friend, you'd just want to know what was wrong so you could help fix the problem. It's not easy to remain open and objective if the rudeness has been going on for a long period and you haven't addressed it before, but it's imperative that you remain cool. When she has stated her case, address her points objectively. If her explanation is weak or unsatisfactory, tell her how her behaviour makes you feel.
Determine what your appropriate response will be.
If your sister-in-law is unable or unwilling to stop being rude to you, choose a path that keeps you from becoming upset by her behaviour and stick to it. On the extreme end, you may decide to stop participating in activities that include her. This action has severe consequences in most families; do not choose this option if it would create more harm than good, or if realistically, you won't be able to maintain the distance.
If a less drastic approach is better for you and your family, simply walk away when she starts her rude behaviour. You don't have to say a word. Go to another room, or join another conversation.
Depending on the severity of her inconsiderate manner, decide if you can simply ignore her. Some people are just hard to get along with, and if you can tune her out and enjoy the rest of the festivities, do so. Be sympathetic towards your brother and continue to be his ally; he may need your support and encouragement.