Seems to me like:
Mom tried to raise her normally, but gave her badminton addiction because that's what she knows how to play -> Mom left her because either she was worried about Ayano's character (of not being able to handle a loss or wanting to be praised and see badminton as a means for it, not an end), or she thought that doing so would be somehow more efficient for Ayano's growth as a player (if Uchika did stop believing in Ayano's potential, she wouldn't try raising more athletes to compete against her) -> Ayano tries her hardest to win at badminton hoping that this will bring her mom back -> loses all motivations she had to keep playing, gives up for a while -> Elena and Kentarou get her to play again, Connie and Kaoruko bring back mom's memories to Ayano (Ayano probably felt replaced by Connie, Connie probably felt threatened by Ayano, at this point in time, both of them wanted Uchika's attention) ->
1) Ayano wants to surpass her mom (giving herself a goal to replace her original one of meeting mom), which isn't going to be easy, she's a 10 times national champion, and cut the bonds between them, with the badminton she gave her (mom might ultimately accept this, because she wanted to push Ayano's potential to its limits, once Uchika recognized it, probably fully accepting the consequences of losing Ayano as a daughter, for the sake of Ayano as the player she wanted Ayano to become; Uchika might've done this out of enjoyment for the sport -- the thing that has taken most of her time and became her way of life --, or to see Ayano go even farther than she did -- in this case, a bit of selfish projection, an attempt to continue enjoying badminton even after she herself can't compete on it, through Ayano, or even as a way to make up for any regrets she might've had as a player), or
2) Ayano trying to surpass mom is still Ayano trying to deal with mom's absence, in a way, Ayano might want to prove that her mom isn't good enough for her, not the other way around.
In a way, Connie and Viggo are interesting characters because of their similarities with Ayano and Uchika, respectively. While Uchika continued putting effort on Ayano, Viggo gave up on Connie; While Connie probably puts effort for Uchika's attention (like Ayano once did), Ayano had her former motivation taken away from her.