An outcast mother of four in an elite society learns that her husband’s vacation to Barcelona is more like a sabbatical from his family. With all four kids suspended from school and are in therapy, she struggles to gain respect in a judgmental society as well as be a good mother.  

Unless Barcelona is important to the story, you can skip that detail in the logline.

Also, you say the lead character is an outcast, but you haven't told us from where she has been cast out.

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"When her husband takes a sabbatical from the family, a small-town woman, new to high society, must help her and her savant children navigate, and adjust to their new community."

Choose one goal, one conflict for me to focus on. You've got several conflicts with several possible protagonists and I don't know whose journey you want me to focus on. Clarity and simplicity always win.