Hi, I wrote pretty clearly that i have a full EU licence and my wife is getting her UK one. She only drives with me in the car to practice.
You seem to be saying that although you have an Italian driving licence (which allows you to drive in the UK) you don't have insurance for that licence? Is that correct.
As said, your US driving licences do not allow you to drive in the UK after 1 year meaning your insurers do not have to pay out if they have only insured you on both your US driving licences. Not having valid insurance is a criminal offence in the UK. If you think the premiums are high now because of your driving offences, wait to you have a criminal conviction for driving, to see how high the premiums will go.
Not telling insurers of anything that will affect your premium, even speeding offences, will invalidate your insurance. As said above, not having valid insurance is a criminal offence in the UK..
You should be insured on your Italian driving licence with your wife as a named driver on a UK Provisional Driving Licence.
Your wife must have a UK provisional driving licence to be allowed to drive and with a valid full driver with her. If she gets caught driving on her US passport only (even with a full driver with her) she will be in court for have the criminal offences of "driving not in accordance with her licence" and "driving without insurance".