Overnight with kids

Has anyone every had their kids stay with them (other than the newborn baby) overnight in the hospital after you had the baby?

My daughter NEVER stays anywhere else but with me and I'm nervous about her staying away when I have her sister.. I would like for her to stay with us, but I'm not sure if it's even allowed. Not to mention it being difficult. Has anyone done this? Please share your experience! BTW my daughter will be 3 months from being 2 !