Pretty sure this is Even Though I’m a Former Noble and a Single Mother, My Daughters Are Too Cute and Working as an Adventurer Isn’t Too Much of a Hassle.
A world where monsters run rampant. A noblewoman falls from grace and loses everything after being falsely accused. But, she started a fresh life as an "Immortal." She became an adventurer capable of defeating disaster-rank monsters and taking the heads off ancient dragons with a single swing of her blade. However, behind that cool exterior... beats the heart of a ridiculously over-indulgent mother!?
"What should I do, my daughters are just too cute!?"
She wields her deadly sword for the sake of motherly love! Ogres flee and dragons tremble at the sight of this overpowered adventurer! The fantasy adventure of the Doting Mother Sword Demon begins now!
The MC is a B-rank adventurer swordswoman named Shirley. She's a "semi-immortal with different coloured eyes and snow white hair," and also a single mother with two 10-year-old daughters, to whom she's extremely devoted.
She was once a noblewoman, but because of her "physical features," she was treated as the "manifestation of an ancient fear" by the nobility of the Empire, and abandoned and betrayed. As a result, she felt she had no other recourse than to be become an adventurer, which enables her to earn a comfortable living and spend plenty of time with her daughters.
The manga is mostly in black & white, with a few pages in full colour.