Just a thought - when your SIL is ok to leave her hospital after 2-3 days usually. While my ds was in NICU and I got discharged on day 2, I refused to go home - well for the first night at least. I slept in a recliner chair in NICU parents lounge. Anyway a NICU nurse took pity on me and suggested to the Dr. to put both ds and me in the pediatric ward - mother's often sleep over in the ped ward. So ds was still a NICU patient but ds's insurance was paying and I could sleep there with him. It was so much better than going home - I had a bed, I got meals and supplies delivered and I could rest and look after my ds.
I think it helped the NICU nurses saw me coming into the NICU every 3 hours and doing his care (temp, diapers, feeds etc). They trusted me and they pretty much left me alone in peds, just checking him now and then. They even brought me a Bf pump to use in ds's room. BTW he just had jaundice and was breathing ok, maintaining body temp by the time they did this. Sounds like your SILs babe does need NICU right now but when he's doing better, it's worth suggesting something like this. It frees up a NICU bed too, and is less work for the nurses.
Also the NICU might have a BF pump room if he's not nursing yet.