I can't answer the poll question without understanding if we are talking about a healthy, stable family or not.
In a stable family, I would say that the primary relationship is the couple. The couple should make sure that their marriage is stable and happy. I don't know that I would call that putting your spouse "first", but if that's what it's called, then yes, the spouse should be first, because a happy marriage means a happier family. And the marriage will hopefully last long after the kids are out of the nest.
Physically the kids take a lot of energy. So they of course take a lot of care, but I don't know that that's the same thing as putting them "first".
I guess I don't really like the term, "putting someone first". Marriage and parenting are joint, cooperative efforts.
If ever there was a situation when I was concerned about the welfare of my children, that's a different situation and I would most certainly put their care over my relationship with any other person, whether that person was their father, grandparent, etc.