Batty- I'm sorry, but if I am just going by your OP, I would say YABVVU.
However, it seems like you left out big significant parts of the story. 1) Your parents have said that the baby being there is going to stress them out, 2) the details of the travel (5+ hours, no room in car, etc.) and 3) the fact that your sister sounds very irresponsible, perhaps either young, or just used to being treated like she's young.
So I'll just say, if the above were not true, I'd stick with you being U. It's a funeral, and having babies there can be a vv good thing. It reminds everyone that life is carrying on, and it is a significant family event after all. Weddings and funerals, bringing us all together.
Your sister sounds like a pill, though, and I've got no idea what to suggest there. Are there no other family members who would consider helping with the baby? Perhaps more distant relatives, cousins or so who aren't as close with the diseased? I've been to funerals for DH's grandparents, I could have easily held on to a baby for a while.
I sympathise with you having to make decisions and arrangements for your sister. I'm an only child, so this is something I have no experience with. If I needed something doing, I did it myself. Best of luck, and I'm sorry about your grandmother.