OP, I'm posting from my brothers house, where I'm looking after his ds5, dd3, and ds1, while they have a two night, three day break away together.
I do this every year, and also at other times.
It's what family do.
I have three adult children, and cannot ever imagine letting you struggle whilst bereaved and pregnant - not in a million years!
Your mum is in the wrong, and should never have offered if she couldn't manage.
It reminds me when I was heavily pregnant with my fifth child, and found out that their father had another woman. He doesn't see them at all now.
The oldest children's father was unhappy I had moved on, and did nothing to help either.
I then suffered years of post natal depression.
It was a bloody struggle over the years, and my dad was a godsend. My mum not so, she enjoyed her parties and days out, while I cried in my flat, unable to leave the house.
Nearly twelve years later, I still haven't forgotten. 
My best wishes to you at this sad time. 
Only rely on people who you can trust, and you know won't let you down, and keep telling yourself that you can do this.
You can!