I’m not sure what you mean by “extended IKEA Tradfri networks”.
The way Zigbee works is that only one device can be the “network coordinator”. The coordinator creates and maintains the network. You can add devices to that network by pairing the device with the network. Homey is typically the coordinator in your network.
Within a network, you can also have 0 or more routers/extenders. These are always on, typically connected to mains. These devices help increase the range of the Zigbee network, as long as they are part of it. So if you have, for instance, an IKEA signal repeater, it will help increase the range of your network, but you have to add this device to Homey (using the IKEA app) before it will become part of your network.
If you have an IKEA gateway, you have to realize that this will also be a coordinator (like Homey). And because a Zigbee network can only have one coordinator, the result is that you will end up with two entirely separated Zigbee networks. Repeater devices that are added to the IKEA gateway network will not help extend your Homey Zigbee network, and vice versa.
To add a sensor device to your network, you have to install the Xiaomi app to add the motion sensor to your (Homey) network. When you start the pairing process from the Homey app, at least in theory, the sensor device has to be near Homey ór any signal repeater that’s part of the Homey Zigbee network. Once the Xiaomi app is listening for devices, press the button on the motion sensor so it will start looking for the network.