From what I’ve seen with other family members’ in-laws and my own, there are so many dynamics going on at once and not everyone is on the same page.
I have two boys and now a daughter and I’m not particularly worried about becoming a MIL. From what I’ve learned one should:
Not have specific expectations or a certain image in the head of what you think your DIL or SoIL will look or be like.
Do not involve yourself unnecessarily in couples’ arguments and if asked for advice, be neutral.
Don’t badmouth or harshly criticise them especially over tiny things.
Get to know DIL and SoIL to a degree of comfort so they are open to a relationship beyond acquaintances (especially before children enter the picture).
Acknowledge and respect boundaries even more so when it comes to home and children. It’s not just your adult child’s home and children.
Come to terms that you might have made mistakes in the upbringing of your own adult child and/or you don’t know your adult child as well as you think so best not to automatically assume the fault is with DIL or SoIL.
Your adult child is not you and may not have the same type of relationship as you and their father or your current spouse.
Be able to accept that the relationship you may have envisioned between you and your in-laws may not happen and the most you can hope and have is basic courtesy and civility.
A lot of it should be common sense, but that tends to go out the window when assumptions and emotions get involved.