I would not be taking my child over there with such an out of control dog. The dog may be small but they can be viscous and can cause alot of damage. I'd be too scared, (and annoyed), to go anymore.
Sadly it seems to sound like your mum doesn't want to be involved in your child's life anyway, and by extension yours, so I would loathe to be making any effort with her.
Also, you shouldn't need to pay for the vets bill - you're telling me the dog became that ill after eating the equivalent of a grape?
I'd be questioning that vets bill if you even want to go down that route. It was simply a situation that occured by mistake!
Your mum should be apologising to YOU for the dogs behaviour!
If it's only your sister you're concerned with seeing, then she could also make the effort to come to yours or meet you out.
Also, your family should make the home safer for your child. They don't need to put all their stuff away but they could make some simple yet effective changes. Though, like I said, I wouldn't be going anymore anyway.
Tbh if someone showed no interest in my child, I would in turn show no interest in them.