Hi OP , it sounds like you are crossing boundaries here, and as the MIL of the mother, this not going to go well for you. you need to let go of control here and you also need to humble yourself and apologise.
it was not your call to make that it was “fine” for your DGC to miss his lunch (that was disrespectful); and you should not have taken the baby downstairs in the middle of the night.
Im personally much more aligned with your style of parenting, but everyone is different and you have to remember that your DIL is still very much finding her feet as a 1st time mum to a very young child. Instead of feeling supported, she is feeling criticised , judged and undermined by you.
She shouldn’t have “lectured” you / spoken to you like a child, and I can understand that will have been difficult for you to take, but also you haven’t shared many details of what she actually said , so it’s hard to judge how unreasonable she was being there .
what do you mean by asking if you “can just be yourself sometimes” around your grandson? If I’m being blunt, this sounds a little emotionally manipulative. Be yourself how? How is she preventing you from being yourself other than asking you to respect/ follow the routines she has for her baby - like mealtimes and bedtime sleeping arrangements? These are perfectly reasonable boundaries for her to have and do not prevent you from being yourself around your grandchild.
Ultimately You hold no cards here, so your best course of action if you want to maximise access to your grandson is to sincerely apologise, and work out how you be a supportive presence for your DIL moving forward .