Congrats! I didn't deliver there but my recommendations in general for the hospital and after:

Hospital:

• You'll be doing so much laundry once you're home, I recommend she just wear the hospital gown during her stay. Fewer items for y'all to wash at home.
• Chapstick
• One never knows if one will need an emergency C-section so if you're a light sleeper, pack a pillow for yourself in case you stay there for 5 days instead of 2.
• If she would like to breastfeed and has the supply, pack a nipple cream she can use in the hospital. It will help after nursing attempts as her nipples will crack from baby attempts at latching, and will hurt rubbing against fabric; before y'all leave, ask her OB for a prescription of all-purpose nipple ointment (APNO). It's around $70 and compounded by a pharmacy. It helps the nipples heal faster.
• in addition to the painkillers she'll get, they'll likely give her stool softener but won't be enough in my opinion. Bring your own so she can take it after each meal (during and after her stay).
• I recommend packing your things in a small rollie bag so you can leave the hospital easily while holding baby in car seat. If mom can't walk, staff can wheel her out. Also, it'll allow you to take more stuff from the room (swaddle blankets, diapers, postpartum stuff, formula samples, syringes).
• Pack either a nursing or pumping bra. If she doesn't have one, you can cut holes in a bra she's willing to sacrifice. Baby will latch easily, other times not and mom needs a mental break so baby is bottle fed; or baby has jaundice and needs formula instead of breastmilk to bring down the bilirubin; or you and mom want a night's rest by having the nurses care for baby while you sleep but mom needs to pump to establish supply or relieve breast pain. In the latter scenario, I pumped in the middle of the night (between 2AM - 4AM), in the dark while my husband slept, for 20 minutes. To stay awake and make time go by faster, I used my phone and not needing to hold the pump flanges on my breasts was a plus. No need to bring your pump - the hospital will have one. Despite the pump box likely saying "don't open until after birth", open, wash, and assemble it so you don't have to figure out the mechanics of it after returning home sleep deprived.

After:

• Have heat/ice packs at home. If she chooses to not breastfeed or doesn't have supply, she will still need to address engorgement pain in her breasts.
• I used adult diapers when I got home for the bleeding and not to pee/poop. You can take the mesh undies/pads from the hospital but I found them annoying because of leakage.

Edit: Pumping scenario at hospital