Here you go. Bookmark that on your phone and have a couple open for when things get sticky and you can't think of anything else to say.
iteslj.org/questions/
I spend my working life getting people (some with very little to say in their own language) to chat in English.
I've been doing this for 26 years, most people do eventually turn out to have interests and opinions, but with some individuals you have to mine harder than usually to get them out.
The best tool you have is your body language. An open, interested expression and stance goes a long way. Any small, facial tip offs that the other person is bored or essentially disinterested will make those less comfortable with sharing their thoughts go into instant hedgehog mode. So practise in front of a mirror if you think she might be picking up on unspoken messages that impact how comfortable she feels with sharing her ideas and opinions beyond the kids.
Just be careful that you add in supplementary questions relating to what was just said, and the odd idea of your own rather than plough through the questions. Cos it can start to feel like an interrogation for the person on the receiving end if you don't.
Also worth bearing in mind... I know your brother wants this, but he may be coming up with "helpful" solutions to a problem she doesn't think she has. She may not be enjoying this anymore than you are. She might be happier with mostly her own company, or at least find her own company better than company that she has little in common with. IYSWIM.
You might both be dreading these sessions for the sake of somebody who had good intensions, but has come up with an idea that allows him to feel better, while the both intended recipient and the good samaritan of his "good deed" are both clock watching and wondering how much longer they can keep a yawn in.
If you have to cancel does she sound genuinely disappointed ? Or is there a hint of politely smothered relief ?