Your sister is being outrageous not allowing your (very sensible and great) suggestion of having your MIL look after baby in a hotel room at the venue.
I think you need to withdraw from being a MOH/coming to the wedding. You’re not being awkward, you’re not being difficult. She doesn’t want baby there, that’s fine…but she can’t then expect you to just leave baby for x number of hours/days. if you are BFing the baby, you simply can’t be away from them for a long time (certainly not at such a young age when you’re trying to establish feeding etc).
I have two DC, and both were BF at 6wks PP. There’s no way I would have left them for more than a couple of hours at that age (and if they were going through a stage of cluster feeding, then forget the couple of hours!).
My youngest was about 10days old when my DB got married and I did double check we were ok to all still go: he/SIL looked at me as if I was nuts and told me that ofc they wanted us all there (if me/baby felt up to it). Another friend had a 4wk old. There were comfy spaces for us to feed the babies and really good facilities. The babies didn’t steal the limelight, we were all there to celebrate my DB and DSIL. FWIW, by the time I went back to work, my DC were 6 and 8 months old…BFing/supply well established so I could leave for a few hours (and express to not lose supply/risk mastitis). If my DB and DSIL said they didn’t want babies/children at their wedding, I wouldn’t have been able to make it.
I understand people wanting child free weddings (their day after all), but I think babes in arms is a different ball game: if you want the parents of a tiny baby at your wedding, you should expect the baby to be with them (or looked after very close by/on site!).