Sending bitcoins programatically without running a node How can I send bitcoins in my web app without running the daemon on my server?
Is there a way to do it? Do third parties allow you to send through them?
Yes this is completely possible. There are services which run fully featured API's that provide almost everything that the client can do.

http://blockchain.info/api

There are other merchant processors which have similar functionality depending on exactly what you want to do also.