Focusing on your use of the word "quickly", I am not sure that is possible. Your statement about "primary physical custody" implies there is a court order from a Family Court or divorce decree that prescribes a visitation schedule which you claim "NY Father" is violating by unilaterally extending visitation without your permission (would you have given it if he had asked?).
You could call the police, claiming "kidnapping" and "interstate" transportation of kids, etc. But since there is a family relationship and some parental rights, and you don't know where "NY Father" and the kids are (Delaware is a small state, but still, it's a needle in a haystack to find someone there), I can see the police not exactly considering this "Amber Alert" material and declining to get involved.
You could file a petition for violation of a Custody/Visitation Order in Family Court by Order to Show Cause, but the father has to be served and a hearing scheduled, and I'd expect that won't happen by next Saturday, let alone September or October. Then you can hash out the violation in court and maybe the "NY Father" can have his visitation supervised or be found to be in violation or something.
But I suspect that the Court is going to find that this one week extension is not so egregious and disruptive during summer vacation as it would be during the school year. Does "NY Father's" parenting schedule provide for some normally extended visitation during the summer like most custodial orders? Is there some good reason not to do do?
Your parenting schedule and interparent communications sound like they could use some work: like it or not, NY Father is a parent and should have REASONABLE access to his kids and the parents should work it out like adults in the best interests of their kids, most kids wanting relationships with both parents. Many NY Family courts offer free mediation. You and NY Father might benefit from this.
This answer is provided under the Avvo.com “Terms and Conditions of Use” (“ToU”), particularly ¶9 which states that any information provided is not intended as legal advice or to create an attorney-client relationship between you and me or any other attorney. Such information is intended for general informational purposes only and should be used only as a starting point for addressing your legal issues. In particular, my answers and those of others are not a substitute for an in-person or telephone consultation with an attorney licensed to practice in your jurisdiction about your specific legal issue, and you should not rely solely upon Legal Information you obtain from this website or other resources which may be linked to an answer for informational purposes. You understand that questions and answers or other postings to the Site are not confidential and are not subject to attorney-client privilege. The full Avvo ToU are set forth at http://www.avvo.com/support/terms . In addition, while similar legal principles often apply in many states, I am only licensed to practice in the State of New York and Federal Courts. Any general information I provide about non-New York laws should be checked with an attorney licensed to practice in your State. Lastly, New York State Court rules (22 NYCRR Part 1200, Rule 7.1) also require me to inform you that my answers and attorney profile posted on the Avvo.com site may be considered "attorney advertising" and that "prior results do not guarantee a similar outcome".
Cops. You go to cops. On Monday when you are supposed to have them, you file a complaint for custodial interference along with a ciolation petition in family court.
Otherwise, there may be a custodial "freeze" taking place. This is a process where the NCP usurps custody by these little deorivations until they become bigger and bigger.
This is a by-product of child support. There is no way to eliminate support payments unless a flup takes place, and this week in DE sounds like the NCP is commencing the freeze.
Be sure you are represented and ensure that you act decisively or else you'll be paying support and enduring "visitation" and being humiliated in family court everytime you appear there.
The lawyer representing you in the divorce and subsequent visits to court is the best person to answer these questions as she is the one most familiar with both parties and the information/documentation that led up to the current state of affairs. I agree with what Mr. Lebowitz & Mr. Lomtevas have both said, but obviously we are looking at this from the outside and are not familiar with the inner workings of this matter. Good luck.
I may be guessing or not licensed in your state. No atty/client relationship exists. I earn my living collecting points for "helpful" answers.
The quickest mechanism for getting the children returned is a Writ. In this case, I doubt that it will help. He will bring them back before you can have it served on him. However, if you file the Writ as well as a violation petition, you are establishing a record of his violations with the court. Should such behavior continue, you may be able to get a restriction or suspension of his visits. The question is, is that in the children's best interest? The two of you should work on resolving these issues. The children should have some extended visitation with their father during the Summer.