Sorry for your loss.
And glad to hear some talking and explaining has helped... you now know better why she wanted to bring the baby (and perhaps have better understanding for her decision? It seems it WASN'T just her being her usual irresponsible self), and she now understands why you would have preferred her not to. Together you found a way forward. Great!
If your solution doesn't work out (her DP's work could make a fuss...) you might be back at square zero... except that you have already established understanding for the situation on both sides.
If it turns out she needs to bring the baby, for whatever reason, I can see three issues: The travelling, the sleeping, and caring for the baby during the service etc.
It would of course be great if you could again work together on finding solutions.
Regarding the travelling, well to put it bluntly, beggars can't be choosers. If it's about discomfort, then I'm sure it can be lived with. Not ideal, but surely better than leaving your sister behind.
Regarding the sleeping, several people have suggested solutions that sound doable. Again, maybe not ideal, but workable.
Regarding the caring during long ceremony, I am certain a solution can be found, if need be right there and then. People are generally v willing to help.
Of course, the real issue might be that you can't work together to find solutions, and that you resent it being left to you in the end to arrange things.
I think it perfectly understandable that you would resent this. And in the long term, I think you should discuss it with your sister.
However, I think the time when everyone is grieving is NOT the right time to call for her to "grow up and take responsibility". However hard it is for you, right now I think it would be worth it for you to forgive her for being who she is, and do everything you can to help her attend the funeral (with baby if so required).
It would be a terrible shame if a family row broke out because your GM died. If your sister couldn't attend the funeral because the trip would be uncomfortable.
I hope it won't come to this - it looks like SHE is trying to find a solution (now that she is aware of the problems). If she can't, then it would be really great of you to help her out.
Hope it all goes well and that you have a lovely service, and that your mum recovers a bit and feels supported all round.