Western Union is easy - all you need is the proper name of the person you are sending to (whatever is on their Cedula as they will need to present ID to get the money).
If you are having to send money on a more regular basis, the best thing is to give a TRUSTED (although if you only keep this account for this purpose with no overdraft there is no problem) family member a bank card from a bank account in your country so you can deposit funds in the bank account and have them withdraw them in the DR (cost - usually about $3 compared to a high percentage when using Western Union). This will obviously not work in the short term since they likely don't have a card from you right now.
One other option is if the person you are sending money to in the DR has a bank account in Canada, you can send them the money via e-mail (by PayPal) and then they just log onto the internet and trasfer the money into their account on the internet and then go to the bank and use their Canadian bank card to withdraw.
You could also send cash with someone you trust on a flight to the DR and have the person you are sending it to meet them at the airport with a bottle of rum
You could also send a bank card to someone this way and then there is not such a risk in sending cash as the card would be pretty much useless without a pin #. Put a post to people departing from your city to the DR in the next short while and then meet them at the airport and give them what you need to send. I did this once with pictures for my husband's family following our wedding since they were returning to Spain - a very gracious man from Montreal helped us out and took the pics and my family met them at the airport. Simple.