I have done many wire tranfers over US10k and it has not been a problem. The normal waiting time for the first one will be 1 week or so but after that 2 to 3 days was the norm. I used Bank of America in the States and Banreservas here in the DR where I live.
This will be standard for all of the major banks here in the DR.
As far as drawing funds out of an ATM here in the DR from an American bank, this is no problem, however please be aware that you will be charged US10-12 per transaction.
However, if you have a BOA account in the States, you can draw cash out of the Scotiabank ATM's here free of charge, to a maximum of RD20,000 per day.