@Kinsei I think instead of "Takuya-san's mom", it should be at least directly translated to "Mom". I feel like it's her being cheeky and blurring the line of "(Takuya's) mom" and "Mother (in law)".
I waffled on that one a lot, actually. I'm not convinced her yandere is far enough along for her to be implying that at this point, and I also think that including "-sama" in her address implies she's just politely referring to the mother of the household rather than anything else. Maybe something like "ma'am" would be more neutral, but... I think it's fine as-is currently. ¯\_(ツ)_/¯
Hello~WelcomeI'm sorryIs Onii-chan around?Oh my, Manami-chanOh, Takuya-san's mom ♡Takuyaー!Manami-chan from the family next door is here~!!!!There was just a bit in my studies I didn't understand...Oh my, you're welcome any time, you know?Takuya-san is always taking care of meI'm sure that boy of mine will shape up a bit if a cute girl like you is coming over, Manami-chan ♪