Smartthings is a multi protocol platform, which is great, but it does mean you have to pay a little more attention when it comes to repeaters. Zigbee repeats only for zigbee, zwave repeats only for Z wave. Unfortunately the SmartThings brand plug isn’t going to help at all with your outdoor device as the plug is zigbee and the outdoor device is Z wave. 
Additionally, when you add a new zwave device, it’s really a good idea to run the zwave repair utility to make sure that your network is operating as efficiently as possible.
So the first thing is to look at your devices and see what mains powered device using zwave will be closest to your outdoor switch. Because exterior walls can be much more difficult to get signal through, ideally you would like this next device to be near a window in line of sight of the outdoor switch.
Then run a Z wave repair utility. Wait until the next day and then check to see if the outdoor switch is working better for you.
See the following FAQ for more details. Start with post 11, then go back up to the top of the thread and read down.