I don't have DILs but I do have a SIL. So far that's all going very well. I hope if I have DILs that will go well too. I don't think there are any guarantees but I'm hopeful.
I am a DIL and I do differently to my MIL. My MIL had no idea of her place, especially as a grandmother. The main lessons I've taken from my experience as a DIL: I will never try to be head of my DILs (or SILs) household, regard myself as an equal (or higher authority) in parenting their children, and I will take an interest in my CIL as a person rather than treating them like an someone who is in my way because they don't allow me to do the other two things (which I shouldn't try to do in the first place).
I know that doesn't cover everyone's situation.