Tim, you are doing the right thing, establishing a line of communication with your children. Like you said, worse case scenario is that they will want to study in America as they become teenagers, despite what mom wants. They will start making their own decisions. Do you use skype to communicate with them? Nowadays these internet cameras have better quality. It's harder when kids are too young to use the internet.
I use the good-old telephone. I have a VOIP plan (similar to Vonage), though one that allows me unlimited calls to landlines in Brazil.
One thing I don't understand: your ex-wife has not tried to cut you off from their life, so you are in a much better situation than other LBPs, but can your kids travel to the US for their summer vacation and stay with you? Like other kids whose parents live in different cities or states?
I agree that I am in a much better situation than most LBPs in that I have regular contact with my children. Largely due to language barriers though, I rarely have a complete discussion with my daughter on the phone (in person we can understand each other MUCH better). The answer to your question is "NO". The only way they would be permitted to visit the United States during vacation was if I dropped the Hague case and accepted Brazil as their country of habitual residence. You must remember that in nearly every case, the first thing the LBP obtains is a court order demanding the return, along with custody, of the children.
