I think times have changed and in some ways not for the better possibly. With the internet there is so much information with articles, books recommendations, videos, forums and it's hard to know what to do right.
We did the strict routine because we had to as we had a baby that nearly died and baptised after 12 hours as on max life support.
We did get home eventually but we were on strict 4 hourly meds for 6 months straight. Could only sleep in cot with breathing alarm for technically the 1st year but I was so highly strung at child not breathing every single night and me having to fly out of bed in middle of the night to BEEP, BEEP, BEEP to intervene for 9 months straight that I didn't have the confidence to remove the alarm until over 2 years old.
So we had a very strict routine and our relationship with MIL did break down completely. Not because baby was unwell but because of constant locking horns over routine and circumstances. She was constantly making digs, even when in hospital I remember the Dr's gave baby the neonatal dummy starting in NICU and MIL saying to me "I didn't think you'd have went with a dummy".
She never stuck to our routine. Coming late and expecting me to wake baby from nap (which I wouldn't do as baby needed energy for next batch of meds), so we'd sit there awkwardly or they'd just leave. She was pissed off we wouldn't let baby "just sleep in car seat" so we could go on a long outing to show off her grandchild to a relative. Did try to explain that sleeping in car seat is unsafe time and again and needs cot with alarm but she wasn't interested and I, we were the problem.
Like PP said what are you adding to visits?
You don't know what she is feeling and she is unlikely to share that with you if she feels gotten at.
Being a mum is hard I think nowadays as theres always a sense of whatever your doing is not good enough. There are so many corners on the internet that will tear apart a method or parenting style, whilst another part pushes it/celebrates it. Its easy to doubt yourself.
You got to parent without this pressure and information overload so consider that when you go on about how chilled your style was.
For whatever reason your DIL has chosen a routine way of parenting.
If you want to be involved and mend this, I'd follow their lead and not go rogue doing your own thing. Once you've built trust then you can freestyle things but that will probably be at school age when she feels less tied to the routine and more trusting of you.
I don't like what you said about asking her to see the kids on their own.
I don't think that's right and I bet she feels right now she can't trust you so the last thing she wants is to leave the kids in your sole care.
Before you see kids on your own you need to focus on developing your relationship with you DIL, not your grandkids.
As there will be no grandkids without your DIL.
So that's my opinion to add into the mix here.
Best wishes x