My MIL is a lovely lady. We've both made mistakes in our relationship, I'd say me, more than her, mainly down to insecurity and immaturity. We have a good MIL/DIL relationship, I think, I hope she would say the same.
The thing that meant the most to me in our relationship, was her flying down to be at my father's funeral. She was there for me, for her son, and to pay her respects. I'll never forget that or cease to be grateful to her for that.
I think a really good starting point for a good MIL/DIL relationship, is realising (from both points of view), that you both come from different family cultures, and things you take for granted as being how it should be done, is not necessarily how the other one will view it. And it's not 'wrong', it's just different. And there's got to be give and take on both sides and compromise.
Also, realising that you both share somebody that you love, and they need to balance between the two of you - and try to make that easy for them, rather than a battlefield. Understanding from the MIL's point of view that your DIL and son are now making their own nuclear family, with their own traditions, and needing time and space to do that, and from the DIL's point of view that their DH is still their MIL's son and they love them very much and still want to be a part of their lives. And that one family does not trump the other families, MIL's family matters, DIL's family matters, and so does the family of DIL and DH. All need time, space, and energy.
And that both of you will make mistakes, some big, some small, some intentional, some not - so you both need to be able to forgive, and also to apologise.
Realising it's a marathon, and all going well, you're going to be tied by bonds of love for the same people for many years to come helps.