beta
I see one of two things going on: Her husband doesn't know what she's up to or they can't have kids.
It seems she's in a hurry, and based on the fact that she says that they are living proper lives, she and her husband may be working as traveling merchants. However, she seems desperate and somewhat sad, so it's not a situation where she JUST wants to reunite with her daughter. Based on the fact that she also dressed like an unwed woman and then ran away while abandoning her daughter, most likely to spite her ex-husband, she does not have a good track record of thinking through her actions. And her quickness to try and paint Yaetatsu as unfit means she's doing this on impulse.
So one theory is that she wants a family with her husband, but he doesn't want children. However now that O-ten is older, she's less of a hassle. So now the mother wants to take the chance that they are settled nearby to take her daughter and basically run away again like they did before, catching both her ex husband and current husband off guard.
The other theory is that the mother and her current husband want children but are unable to have any. This one is meh, but it's not impossible, especially because O-ten is their biological daughter and they can still raise her since she is five years old. This explains her insistence on Yaetatsu being a fake father, which she's crazy to think because he's the one who stepped up for O-ten. Yes, Yaetatsu is not perfect, and he's committed many mistakes but he's taken responsibility.
But let's appreciate how Yaetatsu would shoulder everything before but now he relies on Toraji (who is willing to do anything for his loved ones). I'm sure Toraji will be the one to mediate and get the truth out, because O-ten deserves to be raised in a loving environment with people she cares about. But also, she already knows the truth to some extent (she knows her mother left her). So O-ten is aware of more than anyone else thinks, and Toraji knows that as her new father figure.