First of all I must say that I live in Turkey so things may go differently here than in the US. Most 'modern' births here take place in a hospital environment and are (strongly) medicalised, but mothers and their babies are usually sent home after 1 day or a few hours (depending on the hospital) after an uncomplicated VB
and 2 days after an uncomplicated CB.
I was suffering from preterm labour, was under medication for contractions and babies' lungs but still had a (3 week postponed) preterm birth at 34w5d. My baby had to go to NICU care immediately since the birth ended in a vacuum operated birth. After a few hours of close observation he was brought to my room. He was a fine, strong healthy newborn that would go home with me in the morning. He was with us all night and nursing fine. However, things went differently since the next morning he had major difficulty nursing, they checked on him and he 'd developed severe jaundice so we were told he had to go into NICU care again. In the first days he also developed a urinary tract infection. He had a total of 10 NICU stay days in his first 12 days, meaning that he came home twice and was sent back twice too. That's equally hard as having him in the hospital for a full 12 days, or even harder emotionally, considering he was 'taken' from us three times, not just once. On the other hand, we had had the opportunity to have him home three nights in his very first days of life, which has been so great and a blessing to all of us and has been great for trying to life bf and bonding.
My second baby was not preterm but had similar issues in the first days/week after birth so also needed NICU care. The story is very similar to that of our first baby.
I would not want to recommend you to keep your (even preterm starting from 34w) in hospital if he's doing fine and considered strong enough to go home. But IF you take him home, you should be very attentive and know which signals mean taking him to the hospital again for a check-up since any newborn with difficulties may need (urgent!) treatment at some point, and preterm infants are more susceptible for complications.
Also take into consideration that visitors should better not come around until your baby is somewhat older and stronger and definitely not when they're suffering a cold.
If you cannot have your child with you at home, it'd be better to accept that and make the best of it all wishing he/she could soon come home to you. I know I've been feeling very useful pumping my breast milk at home and while visting in hospital (was not allowed to self-feed) every 2/3 hours to provide for my baby! That really empowered me a lot. We've been always very positive about it when our babies were in NICU, I mean we tried not to worry and to be convinced he was in the best medical care he needed, even while knowing he was missing all of our tender loving parental care because of that, it really helped us get through it.
I hope you can guard of further preterm labour until your child is ripe enough to be born. Success! It must also be very hard for you physically, so take care.