I'm upset that my mother-in-law accepted a job at my son's old school
That seems odd. Why would you be upset about her accepting a job there?
I think it's a terrible school and the fact that she accepted the job upsets me.
You not liking the school has nothing to do with your mother-in-law needing a job. She's not going decline a job just because you aren't a fan of the school. Don't put your relationship in jeopardy over such a petty reason.
But I'm still annoyed. I don't think she should work there.
You can dislike the school and still be happy for her. It's not right to be upset at someone for getting a new job.