The first (obviously not my fault) the inflator valve stuck and inflated my suit uncontrollably fast. Even had I been able to disconnect the hose (I couldn't due to the thick gloves I didn't want to wear) it all happened so fast and the force of the air made it nearly impossible to even move my arms enough to grab the hose. After the incident I was given a different dry suit to wear for my second dive.
It can take practice to learn how to disconnect the hose. I couldn't do it when I first started using my drysuit (I use 5mm gloves) but practiced it a whole bunch the first few times I started drysuit diving and can now do it easily - which came in handy on the weekend when my suit had the same malfunction as you! I am really surprised that the air made it impossible to move your arms... When you move them it should cause air to vent out the suit (can happen via dump valve or wrist/neck seals, in my experience) and free up your movement. With more experience you should be able to respond quickly to this so my advice is to practice
I just ripped out the hose straight away, went vertical and pulled open my neckseal, and didn't really start to ascend at all. Though as my inflator button stayed stuck this let half the ocean into my suit
But better than an uncontrolled ascent.
Anyway, I got my inflator serviced, was sand in the valve so that could have contributed to it sticking. Sounds like you might have a dodgy one. The second dive sounds like another malfunction. It really helps to have your own suit as drysuits can be fiddly with fit and so on, and rental ones might not be very suitable at all.
If you are nervous (and I can understand why you would be!) perhaps go practice all the drysuit skills in a swimming pool/shallow dive until you are comfortable. See if your AOW instructor can help you with this.
On drysuit versus wing for buoyancy. Well I used to only use the wing for buoyancy but not any more. I tend to overweight myself slightly so I can keep more air in my suit for long dives, just keeps me warmer. It is really not difficult to manage buoyancy in a drysuit (I was told by others to only use wing for this reason so I avoided it for a long while) so I think it really comes down to personal preference as to what people use. There is no correct way despite what a lot of posts on Scubaboard say
I think people should be taught the pros and cons of either method and then they can make up their own mind. Some people seem to run the suit with so much squeeze that it defeats the purpose of thermals as there is no air to loft the undergarments...
It is also interesting to read that a number of people think that water in a drysuit will cause one to sink. Not sure why that seems to be such a common belief?? I have had SO many arguments with people about this trying to convince them that a flooded drysuit is not negative