I won’t be able to give a legal opinion but personally I feel like telling your mom will never be the right decision until you’re able to provide for. As long as she’s dependant on your father for financial support she will have to live with him, so knowing will just make it harder on her.
To tackle the problem now the best way would be to either confront your dad separately or send an anonymous message stating that you’ll expose the affair and he will end it hopefully.
Potentially in the future when you are earning enough you can take the step to take care of your mother and let her live with you, letting her leave your father. I know how hard it would be for someone who you idolized or loved your whole life to end up doing something like this, even if he is having an affair you still love him and it will still be hard to take that step.