Ayako likes to tease her twin brother about his affection towards Tatsuya, choosing to word things in a way that would normally cause misunderstandings.
However, the two of them get along well. Ayako and Fumiya are usually paired up in gathering information on various things.
Ayako holds a close, yet professional, relationship with Tatsuya. She is one of the few Yotsuba family members who does not look down on him, and is one of his main sources of information.
During the Reminiscence volume, she had shown tsundere traits of admiring Tatsuya, but it is unknown whether these feelings have changed since then.
It has been hinted that she has strong feelings for him, believing that he is always protecting her and feeling gratitude to him for teaching her how to use her innate magic, and therefore allowing her to establish herself as a great magician. As such, she has never looked down on him as a mere guardian. She also overestimates his abilities.
In Yotsuba Inheritance volume, Ayako walked out from the family gathering after Maya announced the engagement between Tatsuya and Miyuki.
She suspects that Maya organized Tatsuya's engagement with Miyuki and announcing him her son, to simply use Miyuki for planning of Tatsuya's future.
Ayako feels intense rivalry towards Miyuki for unstated reasons, but the reasons can be guessed easily based on their circumference.
In the Steeplecross Arc, since Miyuki feels jealous easily in regards to her brother, she dislikes the fact that Ayako's ability for gathering information can help her brother unlike her power that is great only for suppression. Ayako is delighted after flaunting about that to Miyuki.
Tatsuya is rather involved in their rivalry, being one of the many still unstated reasons.
In Isolation chapter, Ayako compares Miyuki with Maya and themselves to Miya and Maya (As far as sisters go), when she was overwhelmed by Miyuki's Freezing magic.