Both agree that Alice can choose her own life, and that Betty has Alice's interests at heart. So straining their relationship by totally disregarding the other's wishes is foolish.
Betty buys a piano for Alice and signs her up for lessons, but seems skeptical that she could pursue it professionally. She pressures her to prioritize her warrior training.
Justified: Alice is young and her ideas for her future are likely foolish or unlikely to succeed. Betty just wants Alice to have a fallback set of skills.
Betty has to badger Alice into doing things other than taking up the family business or following in Betty's footsteps.
Alice thinks that her mom shouldn't pursue a degree or get a job once all her children grow up.
Subverted: Betty encourages Alice to experiment and do the things she loves best.
Double Subverted: ... but secretly sabotages all these attempts to drive Alice into willingly doing what Betty wants.
Parodied: Alice fights tooth and nail to play the piano... and she sucks. Betty wants Alice to be a warrior because she think's she'd be successful at it... and she sucks at that too!
Zig Zagged: Betty disapproves of Alice's hobbies, but it's only teasing. Alice prefers her hobbies to what her mom wants her to do, only to realize she doesn't like those hobbies and is doing it solely to rebel.
Averted: Alice doesn't have hobbies that distract her from her true calling, and Betty wouldn't mind if she did because they help round out a person.
Enforced: This is a coming of age story and there has to be inter-generational strife to overcome.
Lampshaded: "Alice, I realize I sound just like my own mother when I say this..."
Alice wants to make Betty angry, so she takes up hobbies that she knows will annoy her.
Betty wants Alice to become passionate about something, so she tries to forbid her hobbies to help her find the one she truly loves.
Exploited: Clara, Alice's jealous younger sister, tells Betty rumors about Alice not training in favor of hobbies.
Defied: Betty knows Alice will resent the strict training regiment she has her under, so she allows Alice opportunities to try new things.
Discussed: "Betty, forcing Alice to follow a path she don't want, and denying her choice won't end well."
Conversed: "You'd think obsessive control freaks in these stories would realize that crushing the dreams of their children in favor of their own just makes it likelier they'll rebel."
Deconstructed: Betty does this to relive her dreams by proxy, which were ironically taken taken from her by a mother doing the exact same thing.
Reconstructed: Alice and Betty live in a world where Alice doing anything but what Betty knows to be best will mean Alice's suffering or death later in life. Like a post apocalyptic world or royal family.
Plotted A Good Waste: Usually this plot is used to make Alice sympathetic and ends with Betty reconsidering her opinion. It's instead used to make Betty sympathetic by showcasing how she better knows Alice's strengths and what it would take for her to succeed, while Alice is oblivious and disrespectful.
Played For Laughs: Alice is awful at her hobbies, and Betty's idea of a good career goal for Alice would make her dirt poor and miserable.
Played For Drama: The strain tears Alice and Betty apart, and leads to both leading unhappy lives.