Ok. It has to be said.
Your sister is using this situation as a way to maintain power over your mother. Any JW knows that in instances where a close family member is disfellowshiped, it remains a "matter of conscience" whether or not the shunning applies. Your sister can maintain a relationship with you and your mom since they are very close family members. However, she choses to apply the "shunning" practice to Martyr herself before the congregation ..."Poor sister so-n-so...she's LOST her mother and her sister...) So she looks like a martyred saint for abiding to the shunning policy. THIS WHEN EVERYONE KNOWS that when immediate family is involved, IT'S ENTIRELY A CONSCIENCE MATTER! (which would give her an "out" to communicate with you two if she really wanted to...but doesn't.)
I've been disfellowshiped for years. My mother (a very active and proud witness) maintains communication with me. She doesn't approve of what I practice, but we do not discuss religion. She respects my change of beliefs and we don't discuss religion. And my children are able to enjoy their grandmother and she them. My mother-in-law ALSO a very active witness, as well as my sister-in-law and her family, also witnesses. They are IMMEDIATE FAMILY....and we maintain a good relationship. We merely do not discuss anything spiritual. And they remain in excellent standing in their congregations. My mother even lets me know that people in the congregation still ask about me and my kids (after 10 years of being out!) and wish me well, although i am not in.
I would try to dig up some watchtower literature demonstrating the shunning policy being a conscience matter, highlighting it...and sending it to her with a note saying...."We can still be a family.....for the kids sake." It might not do a lot of good, but at least you'd be able to know that you put the WTS's words in front of her, letting her KNOW that the reason she shuns you is not because THEY'RE banning her...but because she CHOOSES to ban you.
Good Luck. I feel for you. My not-so-immediate family still shuns...and i really miss them.