You hated laying on the guilt but in this case it was entirely necessary. How many children can say that they have such a close and loving relationship with their father after a divorce? You offer them something special, important and valuable and this should never be underestimated.
Your ex wife is playing to her strengths, she lost the battle legally but intends to win the war via emotional blackmail and trickery. She is brilliant at it but it is unfair to use children as pawns in this way.
I would go back to the lawyer and ask her to reitterrate the agreement and point out that putting pressure on the children to break the arrangement is unacceptable. If there are any legal consequences it may be worth pointing them out to her. It may give her pause for thought. Showing the children the agreement was an excellent idea and sets a valuable president for future visits. It shows that this is not a choice they need to make it is a legal requirement that they must follow. They need not feel guilty this is something that was agreed by you and their mother. It also empowers them and gives them the reason to say no to their mother.
All you can do is reassure them of your love and how important this is. The first instance is the worst she was hoping you would cave in and comply, the fact you didn't is important. I don't think this war is over but you have made a stand. You sound like you supported each other, making tough decisions isn't easy and the short term distress will be less significant than the long term benefits of their relationship with you.
Make sure that when the children come over you make plans too you are entitled to assume that they will be there for the weekend make sure that your ex is aware that these plans are non negotiable.
I'm sorry it was hard but please believe it was worthwhile.
