I completely understand why you feel awkward about this - this is the sort of thing I would get stuck in and wouldn't know how to get out of.
I wouldn't give any reasons such as the boys don't get on, or anything. At worst it might make the Mum feel bad about her boy's behaviour and upset her.
Or it could lead to her trying to make excuses, promising to get him to change and then you'd be stuck with either becoming even more forceful "I don't care if he changes or not, I still don't want to do this" OR giving in and accepting him, resulting in a potentially cringey situation for you all with him knowing you have criticized him, and him trying hard to be friends with you all...
I think in an ideal world, you should just say "This isnt working out for us any more, we've had a change of circumstances". But, if you're a weakling like me, I'd probably go for a lame excuse such as "We've decided to use the bus" or "I've changed jobs so I'll be going a different way / leaving at different times"
Basically, don't give her any excuse that gives her room to negotiate. You're stopping this, there's no room for discussion. You're very sorry. End of.
At the end of the day, it's not your problem how they get their DS to school. He is not your responsibility, and if his Dad has to leave earlier for work or travel further each day, that's their own business.