Aria is Uni's mother and their relationship status is quite vague; however, Uni has been shown to love her mother very much, willing to take leadership role as Boss of Giglio Nero Famiglia in her place. Aria also cared for Uni, as she gave her position as the Sky Arcobaleno to her so Uni could have a chance to be freed from the curse that shortened her lifespan by taking part in the Representative Battle of the Rainbow.
At first, Gamma was in disbelief that Uni was Aria's daughter; therefore, he grabbed her and wanted to kick her out of their base. However, at their first meeting, when Gamma saw that one of her sleeves was wet, he realized that she had been crying and had hidden her tears by wiping them on the sleeve, which is similar to what Aria had done shortly before her death. After that, Gamma quickly saw the similarities between Aria and Uni and was then completely protective and loyal to her, calling her "princess." Uni and Gamma share a close bond that is perhaps more than normal boss-subordinate relationship. Reborn had also stated that Uni is fond of Gamma, and Uni herself said that she loved him as Aria did. She has also stated that, to her, Gamma is like the mother that she had lost. Gamma also cares deeply for her and has been shown to be unable to decline Uni's requests, like when Uni decided that Byakuran and the Real Six Funeral Wreaths would be her representatives along with him, Nosaru, and Tazaru, and also when she agreed to form an alliance with Tsuna.
When Uni asked Tsuna to protect her, he, at first, panicked and hesitated to accept her request. But eventually he, and the others, agreed to protect her. She became his mentor during the Primo Family Arc and he protected her throughout the duration of the Future Arc. When she died, he was angered greatly and stated that Byakuran was unforgivable for killing Uni.
Byakuran was the one who sealed Uni's soul in order to get all the Arcobaleno Pacifiers and the two famiglias to combine into the Millefiore. He used Uni, referring her as his toy, and was angered when she died in the Future because she was the link to the Pacifiers.
Even though he treated her wrongly, she still asked the younger Byakuran, and his Funeral Wreaths in the present time, to be her representatives in the Arcobaleno battles along with Gamma. She harbor no hard feelings to him for what he did do in that Future and they appears to be on better terms than they were in the future, to the point where Uni trusts Byakuran's judgement to form an alliance with Tsuna in the Representative Battle of the Arcobaleno and genuinely concern from the bottom of her heart of his well-being. The present Byakuran also returns her feelings the same, revealing that her kindness is what connected him back into reality and expresses his desire to protect her, showing that he cares for her.