OK, thanks for that.
When one belongs to a labour union, that union has the sole right and obligation to represent the member as against the employer. If the union isn't doing its job then the remedy is to sue the union. Yes, that's very dicey and problematic if one likes one's job.
Firstly, unless you have any direct evidence that the co-worker's diatribe has a component of racism, that's not an issue. Nor is the mother having ties to the school administration, as the school doesn't want to touch this because it's a union matter.
If the school disciplines the co-worker, then she'll instantly be on the union to grieve it because even if what she was disciplined for is true there's no direct breach of employment contract or performance of employment duties. Yes, the employer has an obligation to keep the workplace safe and productive, but they can't write up everyone for every allegation of "gossip". I appreciate that you consider this far more weighty than gossip but that's how the school will view it.
So your wife needs to start pushing this issue with the union, saying that the co-worker is creating an atmosphere that's not collegial, and is in fact contrary to the spirit if not the letter of a unionized work environment. I'll bet that the union has some internal mediation process for disputes between members that affect the workplace but aren't of such seriousness as to invite discipline. The union has more of an interest in its members getting along than the employer does in its employees getting along.
If your wife is getting no results then she needs to start going higher up the chain of command, eventually threatening to sue the union for not protecting her from slander from fellow member about her own performance on the job.
It strikes me that this isn't what you wanted to hear. There are no easy solutions to this kind of problem. If there's more to dicuss then please reply. If I've answered you then I'd appreciate a positive service rating please.