Sorry, but details are important. Would you rather have people making wild guesses or trying to establish the facts to provide useful advice?
The scenario is described above. If you want visitation, you're going to have to file in Peru - if you even have grounds to do so - unless by some very odd circumstance, Mom granted jurisdiction to VA. But you're not going to be able to figure that out by yourself - you really need an attorney to review your documents to see if there's any hope at all, but frankly, it is very unlikely that you can do anything in VA.
As you were told, DCSE is about the child - and getting the child the legally mandated amount of support. If you don't want to support a child, I would suggest that you stop having sex.
As for 'many men are going through this', that's your imagination. I would imagine that the number of men who stupped a woman who wanted to flee to Peru before the child was born - and then who make absolutely no effort to see the child - and who do not properly appeal an erroneous order- is fairly small.