What do you mean 'send the blood to America'?
Professor Nicolaides is a leading doctor in this area, he practices out of the Fetal Medicine Centre in London. He is a private doctor, but his success rates are so good that some people choose to go to him.
There is the option of the Harmony test. Again, as far as I know this is only available privately and I am not sure how well it works for twins. It isn't a diagnostic test, but will give far more accurate odds. Most people get a risk something like 1/10,000 from Harmony. If you are interested in this, ask in a specific thread. Lots of people know lots about it.
Is it Harmony you think you are being offered now, or just another go at getting the normal blood tests done?
With CVS, have they explained that they will do it under constant scanning? They don't just stick the needle in.
What would you do if you found out that one twin had Down's syndrome? If termination would never be an option for you, you don't have to have further investigations. Or you can choose to wait and have amnio later on (and after the anomaly scan) so you are prepared for any complications at delivery.
As I mentioned, I've had amnio not CVS, but can talk about that a bit if you want me to.