I'm confused about when to use twoje and nasze? Is there a rule or are they interchangable?
I believe you wanted to compare "twoje" and "wasze", because "nasze" means "our", so it's definitely a different thing.
So "twoje" is singular 'your', and "wasze" is plural 'your'. So basically it's just a matter of who you are talking to/referring to.
For example even if you're talking to your friend John, you may say "twoje dziecko", having just him in mind, or you may say "wasze dziecko", treating it like "your wife's and yours child". If you're talking to both parents, you really should say "wasze dziecko".
The 'p' in 'pije' is cut off in the slow form of the audio. Not sure if this can be fixed, but it makes it sound like 'je'.