If the Resto and trans shop are such buddies, they should work something out together. The Trans shop could do the job at cost for the Resto shop, and the Resto shop needs to take some responsibility that either someone forgot to reconnect the line or did not engage the line fully causing it to come off. Im sure there has to be some effort to disconnect the lines, not just a mere bump. A mere bump would knock it off if it was not fully engaged. So its technician error. Im sure you paid some big bucks to get your car done, and this shop needs to realize that they were last to touch it, and that the stereo shop is not going get under the transmission to disconnect the line. BTW, do you know if it was disconnected at the Trans or at the cooler?
Your stereo installer should have routed the battery wire along the firewall, inner fender, to battery. Don't understand why it was attached to a hose of any kind if that is what happened. However, that is not the cause of the trans line getting disconnected. Common sense would dictate what happened. Have you tried the Jiffie Tite fitting yourself? See how it is connected and disconnected. Im sure its not easy to disconnect by a mere bump. Demonstrating that zip tying something on the line will not make it come off. I bet if you grabbed and pulled the hose, if properly installed, you would break the hose before it gets disconnected.