I have a double concrete utility sink in my basement. I love the size and want to keep the sink however the drain leaks when I use the sink. I used a wire brush to get the rust and build up off of the bottom of the drain and found the drain to be very corroded. The drain is embedded in the concrete tub so I do not know how to install or attach a new drain fitting. Also the pipe that the drain connects into goes directly into the concrete floor and is now moving up/down and side to side (now that I got it disconnected from the sink drain.)
So the question is how to fit a new drain into the concrete sink and is it a problem (if so how to fix it) that the floor pipe can move as much as it does?

I can't figure out how to upload pictures but if you search old cement utility sink on google images you'll find pictures of what I am dealing with.