Yanbu and I say this as the mother of four boys!
I know any future dils will probably want to see their parents first and may even want me to wait a few days, and I will respect that because I remember what it was like and she is priority as she has given birth!
I hope I am bringing my son's up well enough that they support their partners at their most vulnerable time.
When I had ds1 my dhs aunt, uncle and mum turned up to the hospital, mil wasn't going to but dhs aunt brought her. I had had a three day labour after weeks of excruciating spd that had led to me being hospitalised, a failed induction at 38wks, to then be induced again once overdue. I was tired, sore, trying to get to grips with bfeeding, bleeding as you do after birth. And it was overwhelming. My mil did bring me some lovely gifts, for the aunt though it was all about the baby, passing him about when he just wanted to feed and I wanted to rest.
They did similar again after ds2, with number three we said no wait a few days, ditto the next two but aunt was hugely offended by this.
My parents visited once I was home from hospital and settled, they did the same with ds2, mil came to hospital after ds2 but she brought ds1 as she looked after him. Fir ds3 I was discharged after three hours, my dad was looking after the elder two, so he welcomed us home, made tea etc and left us in peace.
With Ds4 a friend looked after the others, he welcomed us home and then left.
With dd I had to stay in a day or so, my mum looked after the others and on her way home she nipped in briefly to see me.
I intend to listen to my dils, I want to support them as they see fit and respect their wishes.
My own mil is lovely, she fussed because it's in her nature to worry, but she cares and is lovely.