There's not many people who think the child's father should be the one at home, looking after his child and not on a week's stag-do!!!!!!!!!!!!!! In my day a stag or hen-do would be a Friday night on the lash round town, i.e. the town where you live and not some random town hundreds or thousands of miles away. A whole week is ridiculous. I thought it a bit much when these things turned into weekends away. If he were single and carefree it might be a different matter, but he is not, he has responsibilities - his 6 month old baby. Also if they are getting married in a few weeks will there be a honeymoon and if so does baby go too? How many holidays does this man want? What about his parents, are they local? Can they look after their grandchild for a few hours?
It sounds very much as if this is a deep rooted family problem, probably going back many years. Maybe the sister bullies their mother and she is trying to do the best she can for everyone.
But really the sooner this woman realises that the only person you can rely on in life is yourself the sooner she will find some sort of peace. If you expect the worst then you will never be disappointed and everything else is a bonus.
I would advise her to get 2 or 3 reliable, paid, baby-siters/childminders teed up for the future (I know this won't help her overnight) but as the child is 6 months old I would have thought that is something she would have had in place already.
Unless her mother is really horrible, which as she had arranged for her to look after the baby it doesn't sound like she is, I would very much advise not to cut ties with her. You only get one mum in life and I would give everything in the world to have mine back (she died 2 1/2 years ago). Every family dynamic is different and no-one knows what really goes on behind closed doors. It is very easy to judge when you are on the outside looking in and only have one side of the story.
At the end of the day a baby is the responsibility of its parents and when one of the parents prefers to go on a week long jolly don't berate the grandmother for trying to accommodate equally the needs of both of her daughters.