Her job might be in danger.
If Catholics are not allowed to participate in non-Catholic weddings—If a Catholic’s daughter is getting married he cannot walk her down the aisle—I would think they would not let a non-Catholic in such a high position.
But they probably went for the most qualified person, and that would be your wife.
Good luck!
For better or for worse, I know that many Catholic schools have non-Catholic teachers and even high non-Catholic administrators.
Here in East Tennessee, where only 2% of the population is Catholic, it seemed the only way to keep the school staffed. That might not be true in all dioceses.
I have not seen the contract, but I think all teachers, of whatever religious affiliation, are expected to publicly affirm Catholic faith and morals. Our school staff has no problem with that.