There seems to be so much excessive drinking throughout our society andn all age groups. I'm not anti alcohol, and being on various meds for RA means I'm limited to a unit a day. I'm with all the other posters, Peaceful Solution (great name by the way, especially given your OP), you seem eminently reasonable. I don't want to sound pompous, but most recent research sadly indicates that the gransnet age group (not the posters, of course) drink rather more than is wise. Your mil must have drunk a considerable amount to have glazed eyes, and be slurring her words by 9pm. Is she on any medication, that could have interacted with alcohol? That wouldn't be any excuse, of course, as she ought to have been extra cautious if that's the case.
I do feel for you, like many of the other contributors to your post, I've first hand experience of a very close relation who has a drink problem. I don't want to be a doom profit, but it does sound as though there's some kind of problem with your mil. I don't think you'll get anywhere talking it through, as problem drinkers are not honest about their consumption, will promise it won't happen again, but it usually does.
Your little boy is the most important person in this sorry situation. You want to keep him safe and secure, good for you. Could you ensure he has some kind of contact with his paternal grandparents, by way of letters, and phone calls. Videos are so easy to make now, you could offer to send them videos of special days out, birthdays etc so they aren't excluded. They could Skype perhaps, that's a great way for families separated by distance to keep in touch. If that goes well, maybe they could rent a holiday cottage again, and have days out with your little one.
Good Luck