Context: I go to uni a half hour train ride away. I live with my mum and 2 brothers, 17 and 11. In exchange for living there rent free I buy the weekly food shop and do the school run on the days I'm not in uni. The 17 year old dropped out of college in December and hasn't started anything in the meantime. Mum is applying to jobs for him but if he doesn't want to do it he blows them off, and he's been doing school run on the days I can't cover since then. I'm in uni 3 days a week, but this week I have tutorial week, so I'm working from home. I also have a group project with 3 other people relying on me to do my part. 11 year old could do it on his own tbh but mum is concerned because he's still in first year of this school, still learning the route, and hasn't done it solo before, and she says she'll let him do it next year.
When 17 year old found out I'd be working from home he told mum that he needed a break from doing the school run 3 days a week because it tired him out and mum asked me to cover all of this week I have off.
The rest of my group and myself planned last week to meet tomorrow (Tuesday) at uni to have a tutorial with our lecturer to make sure we're doing the presentation right and then to work on it as a group. I told my family that I had plans on Tuesday and they were non-negotiable because I booked time with my course leader and had to work on the group project.
Last night my brother came downstairs when I was working on another piece of coursework (I have 3 pieces of 2000 word coursework due during the first week back and then another 2 pieces the week after). He told me how tired taking 11 year old to and from school made him, and how little he liked doing it. Like it was something I enjoy. We had this huge fight where he basically said he didn't want to take 11 year old tomorrow because he was too tired and I said that I would do the other 4 days so long as he covered the one day I had to be in to meet my lecturer(s)/do my group project. He stuck to the stance that he was "just too tired".
Today 17 year old texted mum to say he's ill. He says he has a headache and it too weak to move but he doesn't have a fever, he hasn't been sick, he's up in his room right now watching TV and not even 10 minutes ago he came downstairs and grabbed half a dozen mini rolls before going back upstairs. He's so clearly faking being sick so he doesn't have to take 11 year old tomorrow.
I've told mum that he could not be more clearly faking, and explained everything that went on last night, but she's taking his side and telling me to stop accusing him of faking. I'm trying to put my foot down here but he's playing it up to mum that he's ill and she's falling for it. She's at work 7-7 every day so she can't come home and see how ill he isn't and she can't take 11 year old tomorrow.
What can I do???