OP, I would stand my ground on this one.
'Mom, I do not want ML at my birthday party. Full stop. You can either scale back the event so that her absence is less noticeable, if that bothers you, or we can cancel the whole thing and just go out for dinner. But I will not socialize with that woman on MY birthday.'
And let your Mom know that she is welcome to invite ML over any time she likes, just not at an event in your honour. That if the event is to honour your Mom and Dad's anniversary, for example, you would suck it up and deal. But you are not prepared to do that for your own event.