Use an Android phone as a dongle with a home router I'm researching the possibility of 'tethering' a spare (rooted android) phone to my home router, to act as a 3G/4G dongle and give my home internet via the phone.

I have found USB to Ethernet adapters on Amazon, but these seem to try to give your phone wired internet from your home network, not the other way around.  Perhaps it's still possible to use these?

Another option is to use an OTG USB cable and connect it to a compatible router directly, the ones which allow you to use a USB socket for a 3G/4G dongle.  Does anyone have experience of this?  

There are a few similar questions on here but none are clear or have clear answers.  Thanks.
My router (Technicolor OEM from TIM) has the possibility to connect a dongle with a SIM in it (It must be TIM though) and use it as a tethering device.