@ cannarali and others thinking teach wants him for herself in the town - she's stuck by (publically and privately) the goal of freeing Rei and helping him escape off to university. However since the author wants the mother to be a "heroine", we'll see a bunch of stuff coming at some point thatll make her look like a martyr or similar in order to whitewash how she's acted earlier in the series.
His mom also won't take the deal because compared to a lifetime of pimping out Rei to Gen's dad as worker then Gen, plus the help at home, it's not worth it. The total value of keeping Rei is more than the value of that cheque, so she will keep Rei, simply because owning him like a slave is worth more value. Plus she emotionnally wants him around. Perhaps if the cheque was around a million she'd do it but $100k is not enough. Rei is good to her for a suicide partner or for a solid 30-40 years of work which at $20k income to her household (as if she'd ever let him leave) is 600-800k plus the after work help at home and the emotional use. And that's conservative, where I am construction pays more like 50-100k. The manga will never show this though, but it's obvious when you read through and look at the moms actions carefully plus how she's been described by Rei.
The mom won't fuck Gen because it would wreck his whole secret love for Rei thing and it would also make her irredeemable whereas the author has said she wants the mom to be a heroine in this so that's out. It's a cliffhanger like the others the author is good at making. Most likely the mom is gonna talk to Gen and maybe strike some deal with him about Rei. For extra bitch points maybe she'll strike a deal to keep Rei trapped under both of their chains for their mutual gain, and join up to get rid of the teacher who threatens to free Rei.
THEORY: It could be that later it turn out like the original dad was an asshole simply because the mom cheated with Gen's Dad and found out Rei isn't his son, thus the dad abused Rei as an outlet for his rage and sorrow until Gen's dad forced him out of town. The two continued on their love affair afterwards under the pretext it was a deal they made to get the abusive dad out, thus making the dad look solely responsible for the whole thing and the mother look like a martyr. This would explain alot of things, including why the mom continues to fuck Gen's dad Years later.