I have also found this to be difficult between my two children ages 7 and 9 but what I find helpful is to have the kids come to our house for playdates so everyone can be involved, my older daughters friends can begin to understand my younger daughters autism better in a more comfortable and her natural environment as well. Then, I make sure they both have playdates of their own and extra curricular activities so they dont just have eachother to rely on but other support systems. :) Good Luck!

Maybe you could schedule a mom and daughter outing with Kat when Sarah is going to spend time with her friends?

for Kat: don’t dismiss her anger at sarah as “ petty jealousy”. At school she’s seeing a lot of her classmates getting the things she wants ( feeling included real friends ) and during the school day she swallows those feelings and let’s them out at home. What are the kids at school like to Kat are they mean to her or do they just mearly tolerate her presence but won’t include her. Is the middle school a cliquefest?Does Sarah’s friends have any siblings who are the same age as Kat? maybe Kat could hang out with Sarah’s friends older siblings so Kat can have a social group of her own instead of feeling like a third wheel start with small outing first. What does Kat like to do? if she’s into theatre or acting she could join an acting class. Improv particularly can be very helpful in developing social confidence cause it’s unscripted like real life. Also is she getting social skills training?

For Sarah: Does she know that Kat has aspergers? if not either explain it to her or have Kat explain it (in way that she can understands). Sarah also REALLY has to keep in mind that people on the autism spectrum have a hard time doing something (making friends keeping friends social skills etc) that nerotypical people can do with little to know effort.