From what I’ve heard from friends trying to teach their kids multiple languages, it’s a pretty tricky situation, just like everything having to do with developing young souls. It’s not a simple issue and there are different schools of thought. Most of them do agree, however, on two things: 1) if done wrong it can have very negative side-effects that may be irreparable; 2) the more languages you add the more complicated the issues become.
As one example, I know a woman who’s parents were diplomats for the EU, so they had her learn the language of each country where they were stationed. She’s been fluent in 7 languages pretty much her whole life and is proficient in many more, but she said that it’s actually very difficult to live with, because she doesn’t know any one language inside and out the way she would if she’d grown up speaking one language. She constantly feels insecure in her understanding of words in her own thoughts and when speaking.
Another family I know are teaching their kids French, German, and English, and the German is the hardest even though one parent only speaks to them in German. They do worry quite a bit if they are doing the right thing and it seems like everyone they know is doing it differently and has different opinions on what’s best.
Another thing is that you always hear that learning languages is so good for your brain, start young etc. but you never hear that learning a new language is an extremely emotional and destabilizing experience. It’s hard for most adults to handle the emotions that come with it, and when you’re a young child whose arguably most important need is stability, it’s not a decision to be taken lightly.
And then after all that, if you don’t practice the language regularly, you’ll lose so much of it, even in your native tongue. So, then you’ve sacrificed the comfort and stability of only knowing one language and gotten very little in exchange.
That being said, the fact that your lessons with your granddaughter would be low-key and not expected to make her fluent or anything followed by her learning more seriously with her mother might be a perfect setup in terms of not causing an upheaval for her.