This question has at least four different aspects to it.
- Linguistic. Someone who is divorced usually refers to his wife as an ex-wife. Widowers refer to their wives as a late wife.
- Legal. If you have concerns about how your legal relationship with your late wife's parents has changed because of your wife's death, please ask someone who is licensed to practice law in New Jersey. That question is outside the scope of this site, as are questions about who might be considered eligible for your children's guardianship due to your marital status.
Genealogy and Family History. The two important questions of genealogy are to determine 1) identity and 2) relationship. This is a contemporary question, so the important genealogical task here is to make a record of your relationship and the history which is taking place now. When a spouse dies, generally the death date is entered in one's genealogy database and / or paper family records. The relationships between all the parties do not change. The children you had together are still your wife's children, and her parents' grandchildren. If you were trying to decipher something that happened in the past, yes, knowing the law of the time and the social customs of the time would be important clues to determining someone's identity or relationship. But for now, if you can't describe your own relationship to your children's grandparents, who else can? Why should you give anyone else outside your circle of grandparents/parent/children the agency to define the meaning of the relationships within your own family's history?
Social. I do understand the confusion about whether you are still the son-in-law of your wife's parents. Perhaps it would make things more clear if you looked at it from the perspective of the other parties. Your children are still the grandchildren of your wife's parents; your wife's parents are still the grandparents of your wife's children.
What happens to that dynamic if you remarry is largely dependent on you.
Blended families choose what their relationships to the extended family members are going to be.
Some grandparents, for instance, give lavish birthday gifts to the grandchildren which are their blood relations, but only give token gifts or no gifts to the grandchildren of the second families. I don't recommend this.
Also, if the relationship between your children and their grandparents is a good one, it would be cruel to cut off that relationship if you married again, and insist that the children of your first marriage had to develop a relationship with your second wife's parents, or have no grandparents at all.
If you are currently addressing your late wife's parents as "mom" and "dad" then imagine how hurt they might be if you insisted that had to change because your wife's death has broken the connection.
I suspect that you have received some criticism from others about how close you are to your late wife's parents. In my experience, children in blended families are much happier when the adults in the family do not discriminate between them, based on their blood relations.
For the linguistic question, I doubt many people would use "ex-wife" or "ex-in-laws" to refer to someone who is deceased. Those terms are generally used in the case of divorce, and in my opinion, it would not be very nice to refer to your late wife's parents as "my ex-in-laws". Your late wife must have had a name, so what's wrong with saying "X's parents" (or, if you happen to marry another woman with the same name, "my first wife / late wife's parents").
If you personally are on good terms with your in-laws, and the three of you want to maintain the relationship for the sake of your children, and your mutual benefit, I don't see why you shouldn't keep up the relationship. The logistics become more complicated if you remarry, but these things can be worked out with compassion and fairness as long as the adults act like adults and communicate with each other.
From a genealogy and family history perspective, as well as the compassionate one, I encourage you to be inclusive rather than exclusive. It's more fun that way.