something that sends the contents of $datatoship to everyone (or anyone) that is connected to $socket
UDP is connectionless. Depending on how you look at it, you're never connected with anyone, or you're always connected with every IP address.
Perhaps you mean "everyone that has previously sent some connect request", in which case you need to keep track of everyone that sent you a connect request (and didn't send you a disconnect request), and send the message to each of those individually. What a connect request might resemble is up to you. It could be as simple as sending a message with the string "connect".
Not relevant to your current dilemma, but you talked of a UDP stream. However, UDP is not a streaming protocol. Each Datagram is independent. They are not necessarily received in the same order as they are sent (unlike streaming protocols like TCP).
Finally, you might need to know that UDP is an unreliable protocol. That means you aren't notified if the delivery of the packet was successful. (Conversely, TCP is a reliable protocol. Communication might not be successful, but you'll know if it wasn't.)