I urge you, as much as possible to take the focus off of your mother, your sister and yourself and focus on your children. It is a blessing that you are here and asking these questions.
In the end, your mother is hurting yes but she is an adult, has known of this situation for years and will cope with it through prayer like she has been already. Your sister is coping, and if she is angry will promptly bow out and go on her way. You are being stressed out at family events but again, are an adult. Your children are being FORMED, emotionally and especially spiritually. Are they hearing from you that living in a homosexual relationship is a mortal sin? If so, how are you presenting it to them that their aunt is living with another woman? You are in a bind that is for certain, how do you teach your children that a lifestyle is sinful and disordered when with their eyes it looks to them as if it is normal and loving?
Jesus has known from all eternity that you would be in this exact situation at this exact time in your life. This is no accident, He is allowing this to happen in your life, He is walking alongside you right now. Take this opportunity to grow closer to Him. I believe the focus needs to be your family only because your children are your primary vocation, and this situation can have a great impact. Please take care as best as you can.