water coming out around the air compressor and rides rough. what could be the issue?

No water in the air conditioning system. If you're seeing green liquid, that is antifreeze likely leaking from the upper radiator hose. If you see something clear or white and it evaporates quickly with no residue, that is refrigerant. Stay away from that as it can freeze eyeballs and cause frost bite.

I do not believe its radiator. In the case that it is refrigerant, would it be more likely that one of the hoses had a hole or that the the leak is from the compressor?

There is a seal in front of the compressor that can leak but normally that happens so slowly the mechanics have a hard time finding it with electronic leak detectors. There are gaskets too where the parts of the compressor body are bolted together but I've never seen those leak. A leaking hose would be fairly common but all you're going to see is the oil residue, typically right next to where the metal fitting is crimped to the end of the rubber hose.

Escaping refrigerant will vaporize instantly. It can look like water boiling, but if it's coming out that quickly that you can see it, the entire system will be discharged within minutes. There will be heavy frost buildup around the leak too. Most refrigerant leaks are much slower and take days or weeks to discharge the system. For leaks that small your mechanic can add dye to the system. Later you search with a black light. The leaked dye will show up as a bright yellow stain that you follow back to the source.