When a parent's primary/preferred language differs from their child(ren)'s primary/preferred language, who should have the most "obligation" to learn more of the other's preferred language?

my lexicon in my native language is not very vast

I'm just trying to think like a parent and that would be enough for me to encourage my rhetorical children to speak their native language more. The more languages you can communicate in and the better you get at it, the more ways you have of looking at the world and connecting to people.

This isn't to say I, the parent in this scenario, wouldn't be working to also learn the second language, but I'm not going to judge someone if they don't have the mental energy left to try to learn a new language after a hard day of work.

I dunno, just trying to think it through.

Obligation isn't a useful reference point here. Any party interested in communicating must make the effort to both understand and be understood.

As someone who was not allowed to learn Spanish as a child, or really second language, i say learn as many as you can.

Inside is theirs, and you need to be less illiterate. Maybe do a course and put in time at home with mom.

Outside is yours. Maybe your mom needs to take a few more courses. If not just abide the rule.

Exceptions are when company clearly has a primary language.

This is a question built for me; my turkish has been deteriorating for 25+ years and I am trying to raise a bilingual (spanish/english) child.

When you speak to your mother, you should speak her language (I assume cantonese?) don't be afraid to mention words you lack in cantonese to her during the conversation so you can boost your vocabulary.

If you also have a child that's learning one language more than the other (because the primary language at school etc), communicate to them in your language, but understand what their needs are in their language, and reinforce it in your language (eg : Her : "Quiero agua" Me :"you want water? Ok, let's go get you water. Here's the water. Drink the water")

You speak yours, they speak theirs. In the same conversation.

That's how a human learns a language. The more you converse, the more you will become fluent in each other's languages.