There are a few people in my life that I can't avoid because they're family, but that I do not care about at all. Yet, from time to time a parent or grandparent will start sharing things about these people, and I know it's polite to at least show some modicum of interest and sympathy, especially if the things I'm told about these people includes bad news. 

So, for years now I've been doing the following: 
 - Use [backchannels](https://en.wikipedia.org/wiki/Backchannel_(linguistics)) to make people feel like I'm listening while they're sharing, and use some non-verbal communication like looking at the person talking and doing facial expressions.
 - Ask a question about the situation, something like 'and how is he/she doing now?' or 'what's next?', and listen to the answer, doing the same things as in 1 to pretend I'm interested in it. 
 - Make a 'sympathy remark' about how the situation must suck for this person and/or that things will get better for them soon. This usually closes the conversation and moves it to a different topic. 

The last few such conversations though, this approach failed. For example, with my mother, after I did the remark about how things must suck and would get better soon, and including a topic change, she just kept on talking about the situation. In the most recent case, it was a cousin that had a baby and trouble afterwards that landed her in hospital again. I followed the script, but after I did step 3 my mother would start reiterating things already told. I repeated step 3, but included a "You mentioned that, yes" before doing another sympathy remark.

At that point my mom called me out for acting disinterested. She knows I don't care about that cousin's side of the family and so I just reminded her of that, which mostly settled it, but she's still thinking I was rather impolite by letting the disinterest become visible. She wants me to improve on this, to avoid future trouble when in such conversations with other family members, because apparently they've been picking up on it as well and telling her. 

Like I said, I don't care for these family members, and usually that would be enough to for me to just dismiss this. But that side of the family has caused me trouble with my mother before, they hold her responsible for my actions to some extent and I do not want any more trouble with my mother over this. So, given that I can't (and won't put in the effort) to do 'real sympathy' towards these people I do not care for at all:

**How can I better fake my way through these conversations in a way that people will think I was genuinely interested and sympathizing?**