I don't think Tsubasa's mom was the r**ist.
1. Kaede knows Tsubasa's last name (Arisaka Tsubasa). Arisaka is not a common name, especially if they are still in the same city. Just hearing her surname when she first introduced herself would've triggered him. Unless her mom re-married and changed names, then it's a whole different story which brings to my second point :
2. Blondie went to the same school as Kaede, and now is in the same school as Tsubasa. By proxy, Tsubasa knows which JHS Kaede went to. If her mom was there, it would've come up in a casual conversation, something like "Oh, my mom used to teach there. She went by (previous surname) before." especially because Tsubasa wants to bond more with Kaede.
So, unless the mom was amazingly deceptive of where she worked and very good at hiding her emotions while at home, I highly doubt it's Tsubasa's mom.
I think it's the home tutor that is yet to be revealed, and she might be the mom's acquaintance or blood relative.
The r**ist teacher might have got blacklisted to teach in public schools, but she's getting by as a private tutor.
Or maybe, the author is just going to do it anyway and make Tsubasa's mom to be the big bad for the sake of drama.
We'll have to see.