You branch off from the copper tubing with a 1/4" compression tee. Cut out a small section of tubing for which the tee replaces. You must use a tubing cutter to do this, any other method will cause the tube to become oval.
Install the short piece removed on the side outlet of the tee. Attach a 1/4" compression x 1/2" pipe thread adapter to the short section. If you can find a tee with a pipe thread side outlet (preferred), skip the previous step.
Connect a 1/2" pipe thread to hose adapter. When buying parts, ensure the male and female parts mate correctly. If you can't find the proper mates, get a short nipple or coupler to change gender. Use several layers of teflon tape on male pipe threads, wrapped in the direction that causes it to get more snug when the pipe is screwed in.
Attach hose and controller. After all this, there probably isn't much pressure left, meaning you could probably transition from hose to 1/4" drip fittings for the run from controller to plants, keeping the installation less obtrusive. If you use pressure adaptive drip fittings, you can better regulate the flow to each plant, otherwise the first plant will get the most water, the last hardly any.
Be careful, though unlikely in this case, as high pressure can cause drip fittings to blow apart. You also can't use most pressure reducers, as they can spill water as they function. You'll probably have to go from hose to 1/2" drip main to 1/4" drip distrubution. The 1/2 to 1/4 punched connection can leak slightly, so it should be done over the first plant.
Best Answer
I'll bet the part on the left looks like the part on the right. One can see the bearing surface on the left which contacts the ball valve. Comparing it to the right side, it appears that the insert is threaded and was unscrewed rather than the desired hex item. Consider to apply a bit of thread locker to the external threads on the item on the left, taking care to restrict it to those threads, or apply thread locker to the internal threads on the left side, without getting any on the ball assembly.
As you should never need to open that section again, red (permanent) thread locker may be a good choice. Blue (temporary) thread lock could break free. After allowing the assembly to cure for an appropriate time (read and follow all label directions), you should be able to remove the hex item as originally desired.