Can this hole be repaired or do I have to replace the hole transmission?

I will assume you are talking about JB Weld or a similar product as "that stuff that gets real hard". If, as you say, it is a pressure line connection that is broken, it is unlikely that it will hold, or can be repaired, if it is the transmission case itself. If it is a fitting or line it can be replaced. Again, if it's the actual transmission case itself that is broken it's almost surely shot. If it's the original transmission and has not been recently rebuilt I recommend finding a quality transmissionn shop and ask if they have a rebuilt trans. You can buy or can they get one for you. If not, or if you need a cheaper solution, try to find a working trans. From a local salvage yard. You might be able to save money by taking one with no converter or tail shaft which you should be able to use off your old trans. As long as it's an identical replacement. The currrent "repair" is likely to come apart on you at the worst possible time. Good luck and I hope this helps.

Disregard the tail shaft comments. Answered too many questions today and forgot which model I was talking about. What you have is actually a transaxle. The rest applies and you do need a replacement or rebuilt transaxle if your case is broken.

Chances are the JB weld will work for a while. However, based on where it is broken, I recommend it is welded (aluminum weld). The best type of welding for aluminum is tig welding (Tungsten Inert Gas).