This is your last warning: spoilers abound.
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Asumu remembers hearing western fairytales. Her parents like them (she'd begged for them as a little girl), and given the sort of upbringing her husband received, it's hardly surprising that Rudolf was stuffed full of fairytales as a child, or that he would repeat those stories to his girlfriend, later his wife. One old tale in particular swims to the front of Asumu's mind: that of fairies becoming enamored of a newborn human baby and stealing it away in the night, to be replaced with a changeling fairy babe, a cuckoo in the nest.
It's… interesting, to say the least.
Battler so resembles his father, and judging from pictures Asumu's seen of him as a younger man, he much resembles his paternal grandfather as well. He has hair the same shade of deep cherry red that Rudolf's is beneath layers of coal-black hair dye. He has a face shaped just as Kinzo's was as a young man. And Battler has eyes as blue as the ocean, something Asumu would like to believe came from her green-eyed self, but in all likelihood is a hand-me-down trait from his gray-eyed grandfather.
He resembles Asumu not at all. He resembles her not at all. He resembles me not at all.
She first started to notice it when Battler neared a year old. Oh yes, he shares personality traits with her, many of them, from a paralyzing fear of moving vehicles to a flat out refusal to claim that the obvious suspect on a television show or in a book must be the killer, just because they're the obvious suspect. He has many of Asumu's personality traits, but Asumu knows that this could be a matter of Battler having learned them from her just as or more easily than it could be a matter of blood.
And he's not of her blood, she thinks, almost certainly not. He looks nothing like her. Battler looks like a mixture of Rudolf and Kinzo and some unknown other, her features filling up the gaps. Nothing of Asumu can be seen in the face of this boy. Moreover, Asumu remembers, just after having given birth, when she was still drifting in and out of consciousness, she could hear the nurses and doctors whispering over her, and could swear that the word "stillbirth" was being passed around often. Her child was stillborn. Rudolf had assured her, over and over and over again, that she'd just been hearing things, but her memory does not lie to her. This is the truth that causes her great pain, but it is the truth. Her child was stillborn. Battler is not the boy she gave birth to. He is not her son.
But in what way is he not my son? Asumu wonders to herself one morning. She's putting the finishing touches on Battler's lunch and he, exuberant six-year-old that he is, bounces around her, impatient to see what she's made for him to eat.
Asumu does not know whose child Rudolf stole, and whose warm and loving arms he took him from (Though she can guess). She does not know where her changeling child came from, and it should not matter. She does not wish to know what became of the son she gave birth of, too afraid is she that she already knows. It does not matter. She does not care.
Battler is her son. He is her son who as a baby would see the sunlight turn her pale brown curls to gold and tug on them with a small, fascinated hand. He is her son whose very firs word was "Mama!", brightly shrieked one day when Asumu came home from a shopping and Battler toddled from his father's lap to greet her. He is her son who learned to read at her side. Her is her son who loves his mother, and is loved in return.
They may not share blood, but changeling or no, Battler is her son in every way that matters. For Asumu, that is enough.
In chapter 7 of the Ep. 8 manga adaptation (I don't know about the original version), Rudolf implies that Asumu may have picked up on the fact that Battler wasn't her biological son, and that she loved him and raised him as her own son anyways. While I'm sure that Kyrie would have been a mother to Battler if she'd known the truth, I also happen to be a fan of the belief that your parents are not the people who conceived you, but the people who raised you (Something I know that not everyone agrees with; make no mistake, I'm not trying to push my beliefs onto you). This particular instance just happened to be a sad and messed up situation that some decided to make the best out of.