If not using it for Alexa connectivity, why not just get an actual intercom? A pair is like 30 bucks on Amazon, no Internet required.
Or "hey Alexa, order an intercom system on my mom's account"
Isn't there an eavesdropping function on Alexa... Maybe it's actually less communication and more checking in on what you're doing (not to increase your paranoia)
As a parent, if my kid said "I don't want to be tracked, I'm concerned about my privacy", I'd get an intercom for everyone in the house and let the Alexa be opt in. Sounds like playing music using Alexa isn't a game changer for you. What does it matter anyway, what if you like headphones better, the Alexa stuff isn't mandatory for playing/listening to music.