Sorry, haven't had time to read the whole thread but just thought I would clarify the legal position for you if still unclear. I am a former solicitor, specialising in family law.
Your ex-H pas parental responsibility for the kids, as do you. PR is not affected by whether the parent has contact with the children. However, day to day, the resident parent can exercise PR independently of the non-resident parent.
Under the Child Abduction Act 1984, it is a criminal offence of child abduction to remove a child from the jurisdiction without the consent of everyone with PR.
The only exception is where there is a child arrangements order (previously a residence order) in force, allowing the person with whom the child lives to take him/her out of the jurisdiction without the consent of others with PR.
There is also a defence that the 'abductor' reasonably believed that the other person consented. Ignorance of the law is no defence.
If you just took them, it might not be an issue at customs. Sometimes customs require a letter from the non-resident parent, but they might not ask. Your divorce papers aren't going to be of any use.
However, if your ex for some reason alerted the authorities, you could be arrested for child abduction (although in this situation I doubt you would be severely punished- more likely to be a caution).
Therefore, unless you have a court order, you cannot go. Some options for you are:
Email your ex, tell him about the holiday (don't ask him for permission) with dates and location. If he does not respond, you can say that you reasonably thought he consented, as you did not hear back from him. Make sure it is in writing for evidence.
Apply to court for a specific issue order under s 8 of the Children Act 1989 requesting that the court grants permission for the holiday. You would be very likely to get the order.
Seek to formalise arrangements by having a consent order drawn up and sealed by the court or apply for a child arrangements order if there is no agreement. This might backfire in case he suddenly becomes interested in the kids again and you have to go through supervised contact and the like.
However, don't just chance it as things can look very bad if you get caught. Hope this helps a little and that you can get things sorted out.