@Sqerly 

From what it sounds like, you have two separate networks that your devices switch between depending on their access. Many smart devices require you to attach the device to a specific connection during setup. The name of this network(the SSID) is the network that the plug will always try to connect to. In order to move the plug to the other network you would have to go through the setup process again. 

Alternatively, most devices can bounce between network when they are give the same SSID or name. On many modern phones and devices, the networks will then only appear as one and the device itself will connect to whatever network is faster. This why many people decide on a unified network or a mesh system. 

  @Sqerly 

This should work fine as control of the smart plugs is not 'local' - meaning that the commands sent to the device are sent: Through the network, then through the internet to Amazon, and then finally back to your network and the plug. Controlling devices in this way means that the switch you want to control does not need to be on the same network as the device you are controlling the switch with. This is what allows you to control devices in vacation homes, or from outside your house, like work.