I think both parties have handled this in damaging ways.
OP its one thing having your parents for immediate support, its explainable although could still be regarded as unfair...but the family chinese with siblings has caused damage to IL's now, its too unbalanced.
IL's shouldnt have text you how they did, theres no excuse. The only insight is theyve probably been upset and anger comes from sadness, so I think they were just very sad.
I wonder did you plan viait times with your parents and IL's befoee birth so everyone knew the plan or has it all just unfolded, if you didnt want viaitors it should have been discussed in advance. Seems IL's assumed theyd meet baby right away and so theres been disappointment.
For a sitting on the fence view, ive always disliked grandparents eagerness over baby and think the new mum should come first and baby second. As if the mum is made to feel comfortable then shes likely to give easy access to baby.
So i think instead of people phrasing it as when can i see baby, if they asked "hope youre ok and resting when you can, let me know if I can get you anything, hope baby is well and i look forward to seeing you and making you a cup of tea when you feel comfortable." - i think thatd get a different response.
This approach of the baby is "their family", like they are claiming rights, just sets off new Mums territorial nature response and they back away and feel uncomfortable.
Im not sure how you will fix this. Id leave communication to your husband for sure.
You say you dont want to be apart from your baby even going in a shower. There are sadly lots of Mums with babies in nicu,hdu,scbu up and down the country with weeks or months ahead of them where they are apart from their baby or.Mums whove experienced the worst, so maybe that perspective that yiu havr a healthy baby and you have came through childbirth with no severe or life threatening complications, that both you and baby being healthy will allow you to dig deep and go in your shower alone from your baby for a short time to let grandparents see baby in the next room with your dh and your parents there to watch over.
On this occassion Id maybe get dh to send them a message:
"there seems to have been a misunderstanding between us all and some hurt on both sides and im sure none of us want that moving forward in what should be a happy time for us all having had a safe delivery for mum and a healthy baby. Can you pop round tomorrow for an hour to say hello at 1pm?"
Id attempt to smooth this over asap and see how they react. Set the next visits every 2-3 days and have dh send them a couple of photos per day to tide them over.
Good luck x