I strongly suspect your mom gives your sister and her kids gifts out of anxiety and superstitious belief that spoiling them/giving them gifts is what is keeping your sister (and also her kids) alive-not that she is aware of this, just that she feels overpowering anxiety at the thought of not giving S gifts and the anxiety is relieved when she spoils S. She doesn’t want you, your brother, her other grandchildren to feel less loved, but then her anxiety kicks in and she can’t control herself. She also may feel a need for you to see S receiving the gifts as she feels you also need to help “take care” of S and feels you will learn from exposure.

So you need to cut mom and sister off from any gift exchanges (no more getting to watch you/your kids open gifts, you will leave the second S or her kids begin opening gifts—which means when mom gets cute and “remembers” a gift in the middle of dinner, you and your family get up and leave).