I have two thoughts about this.
1. Who is responsible?
2. Regardless of responsibility, what's the "right" thing to do given the circumstances?
These are different things and where I sit depends on my mood.
Your mum is responsible for the bill as the home owner
It would be "nice" for your ex to do something to acknowledge his rent free existence but not obligatory without a lease or contract.
Whilst I know it's easier said than done, I think it's up to them to discuss and you should direct each of them to each other and not you.