I can only comment on my own experience of similar.
I had twins born 9 weeks early, they spent 6 weeks in nicu. I was poorly myself, but wanted to see my parents the next day, as I just wanted my mum. My parents briefly saw the babies in the incubators for 10 mins. My DH's parents didnt visit the hospital until 1.5 weeks after the birth. I love my in-laws, but I felt like death, very vulnerable and I just didnt want them there, regardless of how lovely they are.
With our youngest, we were out of hospital the following day. I missed out on so many experiences with our twins, and we both craved time with our newborn alone.
My parents visited 5 days after DS was born. Their visit mostly was them doing the washing, helping with our older DS's and just giving me, DH and newborn time to bond. To my recollection, my parents didn't hold DS on their first visit. There was no expectation that we had to host them etc.
I also had a strong desire to keep hold of baby (maybe a trauma response from the birth i experienced with my twins- they were taken away immediately- i didnt see them or hold them for 24hours).
My parents didnt push this when I said I'd rather not hand him over for cuddles yet.
My in-laws came on day 6. Mainly because they knew my parents had been and just didn't feel I could say no. I regret us not being stronger on this. (I caveat this- I love my in laws!!!) They came, my MIL took DS out of my arms and he was then passed around for over 2 hours between my in laws and SIL. 6 days post csection, I hosted them, making tea & biscuits, whilst not feeling like I could ask for my baby back!
My DH also had little say, as they ignored our other DS's who were still very little and he had to supervise and care for them, as i was unable to due to my csection.
It wasn't a logical feeling, more of a primal gut feeling that i felt uncomfortable with them man handling my newborn. I didnt want them holding him at all to be honest.
I would say, if they decide to hold out on visitors, that you need to respect their boundaries. Even if they have allowed DIL's parents to visit already. She may not understand herself why she feels how she does, so be patient and respectful of their wishes. Please don't expect to hold the baby and if its not offered dont make them feel bad.
I say this as a mum to only boys... if my boys ever become fathers and have kids, I fully intend to not be onto of those monster- MIL's that seem to be all over mumsnet! I fully understand that there can be a huge unspoken difference between your own mum and MIL, regardless of how wonderful the MIL is!