I am assuming the OP and the bride are in the UK but if I were going to attempt to have another rational discussion with a sister I'd been close to for decades before this incident, I wouldn't be saying I CAN'T leave a baby this age.
People can and do for various reasons - in the US, for example, the OP could even be about to return to work. If you have older children, it's sometimes the case that it is unavoidable. The OP's family circs may be such that she doesn't have an ally here.
I would be saying that I had no idea physically what state I'll be in and how the baby is getting on with feeding etc, that having them at least in the same hotel offers a much better chance that I could participate in the event smoothly, if that is her goal.
It's hard to believe the bride could really think the MoH coming and going from the event throughout the day for long periods would cause less comment, which I would also be emphasizing and that if she is hoping that the baby will be 'fine' and the OP won't end up going to the other hotel she needs to know this is very unlikely to be possible.
I also agree that the OP and her DH not being there at all is what is going to cause the most comment, which I would be saying to her as well.
This is all more consideration than the OPs sister deserves but in the interest of my own well-being and family harmony I would be making an attempt to dial down the drama.